Dual gauge field theory of quantum liquid crystals in two dimensions
Abstract
We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this 'deconfined' mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modesmore »
- Authors:
-
[1];
- Keio Univ., Kanagawa (Japan); National Institute for Materials Science, Ibaraki (Japan); RIKEN Center for Emergent Matter (CEMS), Saitama (Japan)
- Leiden Univ., Leiden (The Netherlands); Aalto Univ., Aalto (Finland)
- SLAC National Accelerator Lab. and Stanford Univ., Menlo Park, CA (United States)
- Leiden Univ., Leiden (The Netherlands)
- Washington Univ., St. Louis, MO (United States)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1368572
- Alternate Identifier(s):
- OSTI ID: 1373121
- Grant/Contract Number:
- AC02-76SF00515; S1511006; DMR 1411229
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics Reports
- Additional Journal Information:
- Journal Volume: 683; Journal Issue: C; Journal ID: ISSN 0370-1573
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE; quantum liquid crystals; quantum phase transitions; Abelian-Higgs duality; superconductivity
Citation Formats
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert -Jan, Nussinov, Zohar, Cvetkovic, Vladimir, and Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in two dimensions. United States: N. p., 2017.
Web. doi:10.1016/j.physrep.2017.03.004.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert -Jan, Nussinov, Zohar, Cvetkovic, Vladimir, & Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in two dimensions. United States. https://doi.org/10.1016/j.physrep.2017.03.004
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert -Jan, Nussinov, Zohar, Cvetkovic, Vladimir, and Zaanen, Jan. Tue .
"Dual gauge field theory of quantum liquid crystals in two dimensions". United States. https://doi.org/10.1016/j.physrep.2017.03.004. https://www.osti.gov/servlets/purl/1368572.
@article{osti_1368572,
title = {Dual gauge field theory of quantum liquid crystals in two dimensions},
author = {Beekman, Aron J. and Nissinen, Jaakko and Wu, Kai and Liu, Ke and Slager, Robert -Jan and Nussinov, Zohar and Cvetkovic, Vladimir and Zaanen, Jan},
abstractNote = {We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this 'deconfined' mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.},
doi = {10.1016/j.physrep.2017.03.004},
journal = {Physics Reports},
number = C,
volume = 683,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 81 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Nematic phases and the breaking of double symmetries
journal, March 2007
- Mathy, C. J. M.; Bais, F. A.
- Annals of Physics, Vol. 322, Issue 3
Liquid crystal phases of two-dimensional dipolar gases and Berezinskii-Kosterlitz-Thouless melting
journal, January 2016
- Wu, Zhigang; Block, Jens K.; Bruun, Georg M.
- Scientific Reports, Vol. 6, Issue 1
Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates
journal, December 2013
- da Silva Neto, E. H.; Aynajian, P.; Frano, A.
- Science, Vol. 343, Issue 6169
Critical Properties of the N-Color London Model
journal, August 2004
- Smiseth, J.; Smørgrav, E.; Sudbø, A.
- Physical Review Letters, Vol. 93, Issue 7
Charged magnetic domain lines and the magnetism of high- oxides
journal, October 1989
- Zaanen, Jan; Gunnarsson, Olle
- Physical Review B, Vol. 40, Issue 10
Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
journal, January 1975
- Villain, J.
- Journal de Physique, Vol. 36, Issue 6
Emergence of charge order from the vortex state of a high-temperature superconductor
journal, July 2013
- Wu, Tao; Mayaffre, Hadrien; Krämer, Steffen
- Nature Communications, Vol. 4, Issue 1
Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
journal, November 2015
- Can, Tankut; Laskin, Michael; Wiegmann, Paul B.
- Annals of Physics, Vol. 362
Topological defects on fluctuating surfaces: General properties and the Kosterlitz-Thouless transition
journal, March 1996
- Park, Jeong-Man; Lubensky, T. C.
- Physical Review E, Vol. 53, Issue 3
Soft elasticity of RNA gels and negative Poisson ratio
journal, December 2007
- Ahsan, Amir; Rudnick, Joseph; Bruinsma, Robijn
- Physical Review E, Vol. 76, Issue 6
Stripe fractionalization: the quantum spin nematic and the Abrikosov lattice
journal, March 2003
- Zaanen, J.; Nussinov, Z.
- physica status solidi (b), Vol. 236, Issue 2
Competing orders in a magnetic field: Spin and charge order in the cuprate superconductors
journal, September 2002
- Zhang, Ying; Demler, Eugene; Sachdev, Subir
- Physical Review B, Vol. 66, Issue 9
Effective field theory of fractional quantized Hall nematics
journal, November 2011
- Mulligan, Michael; Nayak, Chetan; Kachru, Shamit
- Physical Review B, Vol. 84, Issue 19
Monte Carlo studies of two-dimensional melting: Dislocation vector systems
journal, December 1982
- Saito, Yukio
- Physical Review B, Vol. 26, Issue 11
Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8+
journal, August 2003
- Howald, C.; Eisaki, H.; Kaneko, N.
- Proceedings of the National Academy of Sciences, Vol. 100, Issue 17
Nonlinear elastic theory of smectic liquid crystals
journal, August 1982
- Grinstein, G.; Pelcovits, Robert A.
- Physical Review A, Vol. 26, Issue 2
Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67
journal, October 2012
- Chang, J.; Blackburn, E.; Holmes, A. T.
- Nature Physics, Vol. 8, Issue 12
Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order
journal, August 2010
- Metlitski, Max A.; Sachdev, Subir
- Physical Review B, Vol. 82, Issue 7
Theory of defects in solids and three-dimensional gravity
journal, May 1992
- Katanaev, M. O.; Volovich, I. V.
- Annals of Physics, Vol. 216, Issue 1
Quantum theory of a nematic Fermi fluid
journal, October 2001
- Oganesyan, Vadim; Kivelson, Steven A.; Fradkin, Eduardo
- Physical Review B, Vol. 64, Issue 19
Classification of point-group-symmetric orientational ordering tensors
journal, August 2016
- Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan
- Physical Review E, Vol. 94, Issue 2
Supersolids versus Phase Separation in Two-Dimensional Lattice Bosons
journal, May 2005
- Sengupta, Pinaki; Pryadko, Leonid P.; Alet, Fabien
- Physical Review Letters, Vol. 94, Issue 20
Phase diagrams of lattice gauge theories with Higgs fields
journal, June 1979
- Fradkin, Eduardo; Shenker, Stephen H.
- Physical Review D, Vol. 19, Issue 12
Absence of power-law mid-infrared conductivity in gravitational crystals
journal, October 2015
- Langley, Brandon W.; Vanacore, Garrett; Phillips, Philip W.
- Journal of High Energy Physics, Vol. 2015, Issue 10
Dislocation loops and bond-orientational order in the Abrikosov flux-line lattice
journal, February 1990
- Marchetti, M. Cristina; Nelson, David R.
- Physical Review B, Vol. 41, Issue 4
Spontaneous breaking of spacetime symmetries and the inverse Higgs effect
journal, April 2014
- Brauner, Tomáš; Watanabe, Haruki
- Physical Review D, Vol. 89, Issue 8
Symmetry of charge order in cuprates
journal, May 2015
- Comin, R.; Sutarto, R.; He, F.
- Nature Materials, Vol. 14, Issue 8
Role of Quantum Fluctuations in the Hexatic Phase of Cold Polar Molecules
journal, June 2014
- Lechner, Wolfgang; Büchler, Hans-Peter; Zoller, Peter
- Physical Review Letters, Vol. 112, Issue 25
Entropy of solid : The possible role of a dislocation-induced glass
journal, March 2007
- Balatsky, A. V.; Graf, M. J.; Nussinov, Z.
- Physical Review B, Vol. 75, Issue 9
Defects in flexible membranes with crystalline order
journal, July 1988
- Seung, H. S.; Nelson, David R.
- Physical Review A, Vol. 38, Issue 2
Frank’s constant in the hexatic phase
journal, March 2007
- Keim, P.; Maret, G.; von Grünberg, H. H.
- Physical Review E, Vol. 75, Issue 3
Bond Order in Two-Dimensional Metals with Antiferromagnetic Exchange Interactions
journal, July 2013
- Sachdev, Subir; La Placa, Rolando
- Physical Review Letters, Vol. 111, Issue 2
Path integrals in the theory of condensed helium
journal, April 1995
- Ceperley, D. M.
- Reviews of Modern Physics, Vol. 67, Issue 2
Deconfining the rotational Goldstone mode: The superconducting quantum liquid crystal in (2+1) dimensions
journal, July 2013
- Beekman, Aron J.; Wu, Kai; Cvetkovic, Vladimir
- Physical Review B, Vol. 88, Issue 2
Field theory of the quantum Hall nematic transition
journal, September 2013
- Maciejko, J.; Hsu, B.; Kivelson, S. A.
- Physical Review B, Vol. 88, Issue 12
Supersolids in the Bose-Hubbard Hamiltonian
journal, March 1995
- Batrouni, G. G.; Scalettar, R. T.; Zimanyi, G. T.
- Physical Review Letters, Vol. 74, Issue 13
Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
journal, January 1999
- Lilly, M. P.; Cooper, K. B.; Eisenstein, J. P.
- Physical Review Letters, Vol. 82, Issue 2
Evidence for a fractionally quantized Hall state with anisotropic longitudinal transport
journal, October 2011
- Xia, Jing; Eisenstein, J. P.; Pfeiffer, L. N.
- Nature Physics, Vol. 7, Issue 11
Solid holography and massive gravity
journal, February 2016
- Alberte, Lasma; Baggioli, Matteo; Khmelnitsky, Andrei
- Journal of High Energy Physics, Vol. 2016, Issue 2
Dislocation-mediated melting of anisotropic layers
journal, January 1981
- Ostlund, S.; Halperin, B. I.
- Physical Review B, Vol. 23, Issue 1
Spin-orbital frustrations and anomalous metallic state in iron-pnictide superconductors
journal, February 2009
- Krüger, Frank; Kumar, Sanjeev; Zaanen, Jan
- Physical Review B, Vol. 79, Issue 5
Topological kinematic constraints: dislocations and the glide principle
journal, July 2006
- Cvetkovic, V.; Nussinov, Z.; Zaanen, J.
- Philosophical Magazine, Vol. 86, Issue 20
Condensation of lattice defects and melting transitions in quantum Hall phases
journal, January 2015
- Cho, Gil Young; Parrikar, Onkar; You, Yizhi
- Physical Review B, Vol. 91, Issue 3
Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors
journal, September 2009
- Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A.
- Nature Physics, Vol. 5, Issue 11
Classification of nematic order in 2 + 1 dimensions: Dislocation melting and (2)/ lattice gauge theory
journal, February 2015
- Liu, Ke; Nissinen, Jaakko; Nussinov, Zohar
- Physical Review B, Vol. 91, Issue 7
Disclinations and first order transitions in 2D melting
journal, May 1983
- Kleinert, H.
- Physics Letters A, Vol. 95, Issue 7
Charged domain-wall dynamics in doped antiferromagnets and spin fluctuations in cuprate superconductors
journal, April 1996
- Zaanen, J.; Horbach, M. L.; van Saarloos, W.
- Physical Review B, Vol. 53, Issue 13
Review on auxetic materials
journal, May 2004
- Yang, Wei; Li, Zhong-Ming; Shi, Wei
- Journal of Materials Science, Vol. 39, Issue 10
The topological theory of defects in ordered media
journal, July 1979
- Mermin, N. D.
- Reviews of Modern Physics, Vol. 51, Issue 3
Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model
journal, August 1977
- José, Jorge V.; Kadanoff, Leo P.; Kirkpatrick, Scott
- Physical Review B, Vol. 16, Issue 3
Quantum hexatic order in two-dimensional dipolar and charged fluids
journal, March 2014
- Bruun, Georg M.; Nelson, David R.
- Physical Review B, Vol. 89, Issue 9
Boson localization and the superfluid-insulator transition
journal, July 1989
- Fisher, Matthew P. A.; Weichman, Peter B.; Grinstein, G.
- Physical Review B, Vol. 40, Issue 1
Topological Defects Coupling Smectic Modulations to Intra-Unit-Cell Nematicity in Cuprates
journal, July 2011
- Mesaros, A.; Fujita, K.; Eisaki, H.
- Science, Vol. 333, Issue 6041
Critical Fluctuations in Superconductors and the Magnetic Field Penetration Depth
journal, June 1996
- Herbut, Igor F.; Tešanović, Zlatko
- Physical Review Letters, Vol. 76, Issue 24
O(2) symmetry breaking versus vortex loop percolation
journal, June 2000
- Kajantie, K.; Laine, M.; Neuhaus, T.
- Physics Letters B, Vol. 482, Issue 1-3
Stripe melting and quantum criticality in correlated metals
journal, September 2012
- Mross, David F.; Senthil, T.
- Physical Review B, Vol. 86, Issue 11
Model of fractionalization of Faraday lines in compact electrodynamics
journal, December 2014
- Geraedts, Scott D.; Motrunich, Olexei I.
- Physical Review B, Vol. 90, Issue 21
An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
journal, March 2007
- Kohsaka, Y.; Taylor, C.; Fujita, K.
- Science, Vol. 315, Issue 5817
Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition
journal, October 2011
- Bernard, Etienne P.; Krauth, Werner
- Physical Review Letters, Vol. 107, Issue 15
Defect-mediated melting and the breaking of quantum double symmetries
journal, June 2006
- Bais, F. A.; Mathy, C. J. M.
- Physical Review B, Vol. 73, Issue 22
Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45
journal, January 2008
- Hinkov, V.; Haug, D.; Fauque, B.
- Science, Vol. 319, Issue 5863
Nematic Fermi Fluids in Condensed Matter Physics
journal, August 2010
- Fradkin, Eduardo; Kivelson, Steven A.; Lawler, Michael J.
- Annual Review of Condensed Matter Physics, Vol. 1, Issue 1
Two-dimensional matter: order, curvature and defects
journal, September 2009
- Bowick, Mark J.; Giomi, Luca
- Advances in Physics, Vol. 58, Issue 5
More on gapped Goldstones at finite density: more gapped Goldstones
journal, November 2013
- Nicolis, Alberto; Penco, Riccardo; Piazza, Federico
- Journal of High Energy Physics, Vol. 2013, Issue 11
Two-dimensional melting
journal, January 1988
- Strandburg, Katherine J.
- Reviews of Modern Physics, Vol. 60, Issue 1
Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field
journal, January 1996
- Koulakov, A. A.; Fogler, M. M.; Shklovskii, B. I.
- Physical Review Letters, Vol. 76, Issue 3
Evidence for stripe correlations of spins and holes in copper oxide superconductors
journal, June 1995
- Tranquada, J. M.; Sternlieb, B. J.; Axe, J. D.
- Nature, Vol. 375, Issue 6532
Type-II Bose-Mott insulators
journal, September 2012
- Beekman, Aron J.; Zaanen, Jan
- Physical Review B, Vol. 86, Issue 12
Order of the metal-to-superconductor transition
journal, January 2002
- Mo, S.; Hove, J.; Sudbø, A.
- Physical Review B, Vol. 65, Issue 10
Experimental Observation of Continuous Melting into a Hexatic Phase
journal, May 1983
- Rosenbaum, T. F.; Nagler, S. E.; Horn, P. M.
- Physical Review Letters, Vol. 50, Issue 22
Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor
journal, January 2010
- Daou, R.; Chang, J.; LeBoeuf, David
- Nature, Vol. 463, Issue 7280
Broken spacetime symmetries and elastic variables
journal, July 2014
- Hayata, Tomoya; Hidaka, Yoshimasa
- Physics Letters B, Vol. 735
Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals
journal, February 2017
- Liu, Ke; Nissinen, Jaakko; de Boer, Josko
- Physical Review E, Vol. 95, Issue 2
From quantum matter to high-temperature superconductivity in copper oxides
journal, February 2015
- Keimer, B.; Kivelson, S. A.; Norman, M. R.
- Nature, Vol. 518, Issue 7538
Topology and nematic ordering
journal, March 1993
- Lammert, Paul E.; Rokhsar, Daniel S.; Toner, John
- Physical Review Letters, Vol. 70, Issue 11
Resonant X-Ray Scattering Studies of Charge Order in Cuprates
journal, March 2016
- Comin, Riccardo; Damascelli, Andrea
- Annual Review of Condensed Matter Physics, Vol. 7, Issue 1
Persistent Supersolid Phase of Hard-Core Bosons on the Triangular Lattice
journal, September 2005
- Heidarian, Dariush; Damle, Kedar
- Physical Review Letters, Vol. 95, Issue 12
Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice
journal, September 2005
- Melko, R. G.; Paramekanti, A.; Burkov, A. A.
- Physical Review Letters, Vol. 95, Issue 12
How good is the villain approximation?
journal, January 1986
- Janke, W.; Kleinert, H.
- Nuclear Physics B, Vol. 270
I. Liquid crystals. On the theory of liquid crystals
journal, January 1958
- Frank, F. C.
- Discussions of the Faraday Society, Vol. 25
Supersolid Hard-Core Bosons on the Triangular Lattice
journal, September 2005
- Wessel, Stefan; Troyer, Matthias
- Physical Review Letters, Vol. 95, Issue 12
Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity
journal, November 2009
- Vojta, Matthias
- Advances in Physics, Vol. 58, Issue 6
A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2
journal, August 2004
- Hanaguri, T.; Lupien, C.; Kohsaka, Y.
- Nature, Vol. 430, Issue 7003
A dynamical theory of elastic dielectrics
journal, January 1963
- Toupin, R. A.
- International Journal of Engineering Science, Vol. 1, Issue 1
Superconductivity in a Strong Spin-Exchange Field
journal, August 1964
- Fulde, Peter; Ferrell, Richard A.
- Physical Review, Vol. 135, Issue 3A
Spatially ordered fractional quantum Hall states
journal, February 1996
- Balents, L.
- Europhysics Letters (EPL), Vol. 33, Issue 4
How to detect fluctuating stripes in the high-temperature superconductors
journal, October 2003
- Kivelson, S. A.; Bindloss, I. P.; Fradkin, E.
- Reviews of Modern Physics, Vol. 75, Issue 4
Phase Transition in a Lattice Model of Superconductivity
journal, November 1981
- Dasgupta, C.; Halperin, B. I.
- Physical Review Letters, Vol. 47, Issue 21
Field- and temperature-induced topological phase transitions in the three-dimensional -component London superconductor
journal, June 2005
- Smiseth, J.; Smørgrav, E.; Babaev, E.
- Physical Review B, Vol. 71, Issue 21
Dual Description of the Superconducting Phase Transition
journal, January 1995
- Kiometzis, Michael; Kleinert, Hagen; Schakel, Adriaan M. J.
- Fortschritte der Physik/Progress of Physics, Vol. 43, Issue 8
Electromagnetic properties of viscous charged fluids
journal, July 2014
- Forcella, Davide; Zaanen, Jan; Valentinis, Davide
- Physical Review B, Vol. 90, Issue 3
Effect of a nonzero temperature on quantum critical points in itinerant fermion systems
journal, September 1993
- Millis, A. J.
- Physical Review B, Vol. 48, Issue 10
Mandelstam-'t Hooft duality in abelian lattice models
journal, July 1978
- Peskin, Michael E.
- Annals of Physics, Vol. 113, Issue 1
What makes a crystal supersolid?
journal, March 2007
- Prokof'ev, Nikolay
- Advances in Physics, Vol. 56, Issue 2
Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
journal, January 2007
- Borzi, R. A.; Grigera, S. A.; Farrell, J.
- Science, Vol. 315, Issue 5809
Theory of Quantum Hall Nematics
journal, May 2002
- Radzihovsky, Leo; Dorsey, Alan T.
- Physical Review Letters, Vol. 88, Issue 21
Theories of elasticity with couple-stress
journal, January 1964
- Toupin, R. A.
- Archive for Rational Mechanics and Analysis, Vol. 17, Issue 2
Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x
journal, April 2016
- Hamidian, M. H.; Edkins, S. D.; Joo, Sang Hyun
- Nature, Vol. 532, Issue 7599
Universal Signatures of Fractionalized Quantum Critical Points
journal, January 2012
- Isakov, S. V.; Melko, R. G.; Hastings, M. B.
- Science, Vol. 335, Issue 6065
Exact results for interacting electrons in high Landau levels
journal, August 1996
- Moessner, R.; Chalker, J. T.
- Physical Review B, Vol. 54, Issue 7
Topology and nematic ordering. I. A gauge theory
journal, August 1995
- Lammert, Paul E.; Rokhsar, Daniel S.; Toner, John
- Physical Review E, Vol. 52, Issue 2
A Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+delta
journal, January 2002
- Hoffman, J. E.
- Science, Vol. 295, Issue 5554
Bulk Solution of Ginzburg-Landau Equations for Type II Superconductors: Upper Critical Field Region
journal, March 1964
- Kleiner, W. H.; Roth, L. M.; Autler, S. H.
- Physical Review, Vol. 133, Issue 5A
Fractionalized phase in an XY–Z2 gauge model
journal, January 2002
- Sedgewick, R.; Scalapino, D.; Sugar, R.
- Physical Review B, Vol. 65, Issue 5
Divergent Nematic Susceptibility in an Iron Arsenide Superconductor
journal, August 2012
- Chu, J. -H.; Kuo, H. -H.; Analytis, J. G.
- Science, Vol. 337, Issue 6095
Anomalous Scaling Dimensions and Stable Charged Fixed Point of Type-II Superconductors
journal, April 2000
- Hove, J.; Sudbø, A.
- Physical Review Letters, Vol. 84, Issue 15
Disclinations, dislocations, and continuous defects: A reappraisal
journal, January 2008
- Kleman, M.; Friedel, J.
- Reviews of Modern Physics, Vol. 80, Issue 1
Diagnosing deconfinement and topological order
journal, February 2011
- Gregor, K.; Huse, David A.; Moessner, R.
- New Journal of Physics, Vol. 13, Issue 2
Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy
journal, September 2011
- Wu, Tao; Mayaffre, Hadrien; Krämer, Steffen
- Nature, Vol. 477, Issue 7363
Observing the fluctuating stripes in high-T c superconductors
journal, December 2007
- Cvetkovic, V.; Nussinov, Z.; Mukhin, S.
- EPL (Europhysics Letters), Vol. 81, Issue 2
Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory)
journal, June 1972
- Kosterlitz, J. M.; Thouless, D. J.
- Journal of Physics C: Solid State Physics, Vol. 5, Issue 11
gauge theory of electron fractionalization in strongly correlated systems
journal, September 2000
- Senthil, T.; Fisher, Matthew P. A.
- Physical Review B, Vol. 62, Issue 12
Nematic Electronic Structure in the “Parent” State of the Iron-Based Superconductor Ca(Fe 1– x Co x ) 2 As 2
journal, January 2010
- Chuang, T. -M.; Allan, M. P.; Lee, Jinho
- Science, Vol. 327, Issue 5962
Melting and the vector Coulomb gas in two dimensions
journal, February 1979
- Young, A. P.
- Physical Review B, Vol. 19, Issue 4
The geometric order of stripes and Luttinger liquids
journal, October 2001
- Zaanen, J.; Osman, O. Y.; Kruis, H. V.
- Philosophical Magazine B, Vol. 81, Issue 10
Colloquium : Theory of intertwined orders in high temperature superconductors
journal, May 2015
- Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
- Reviews of Modern Physics, Vol. 87, Issue 2
Isotropic to anisotropic transition in a fractional quantum Hall state
journal, August 2010
- Mulligan, Michael; Nayak, Chetan; Kachru, Shamit
- Physical Review B, Vol. 82, Issue 8
Hamiltonian approach to lattice gauge theories
journal, June 1979
- Horn, D.; Weinstein, M.; Yankielowicz, S.
- Physical Review D, Vol. 19, Issue 12
Critical behavior of 3D Z ( N )
journal, February 2014
- Borisenko, O.; Chelnokov, V.; Cortese, G.
- Nuclear Physics B, Vol. 879
Charge Order Driven by Fermi-Arc Instability in Bi2Sr2-xLaxCuO6+
journal, December 2013
- Comin, R.; Frano, A.; Yee, M. M.
- Science, Vol. 343, Issue 6169
Quantum Theory of the Smectic Metal State in Stripe Phases
journal, September 2000
- Emery, V. J.; Fradkin, E.; Kivelson, S. A.
- Physical Review Letters, Vol. 85, Issue 10
Condensing Nielsen–Olesen strings and the vortex–boson duality in 3+1 and higher dimensions
journal, March 2011
- Beekman, A. J.; Sadri, D.; Zaanen, J.
- New Journal of Physics, Vol. 13, Issue 3
Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973
- Kosterlitz, J M; Thouless, D J
- Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
Properties and detection of spin nematic order in strongly correlated electron systems
journal, January 2005
- Podolsky, Daniel; Demler, Eugene
- New Journal of Physics, Vol. 7
Foam Structures with a Negative Poisson's Ratio
journal, February 1987
- Lakes, R.
- Science, Vol. 235, Issue 4792
Phase diagram of and U(1) gauge theories in three dimensions
journal, May 1980
- Bhanot, Gyan; Creutz, Michael
- Physical Review D, Vol. 21, Issue 10
Quantum Smectic as a Dislocation Higgs Phase
journal, July 2006
- Cvetkovic, V.; Zaanen, J.
- Physical Review Letters, Vol. 97, Issue 4
What drives nematic order in iron-based superconductors?
journal, January 2014
- Fernandes, R. M.; Chubukov, A. V.; Schmalian, J.
- Nature Physics, Vol. 10, Issue 2
Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field
journal, February 1989
- Fisher, Matthew P. A.; Lee, D. H.
- Physical Review B, Vol. 39, Issue 4
Anyon Superconductivity and Charge-Vortex Duality
journal, October 1991
- Lee, Dung-Hai; Fisher, Matthew P. A.
- International Journal of Modern Physics B, Vol. 05, Issue 16n17
Bemerkung �ber die angen�herte G�ltigkeit der klassischen Mechanik innerhalb der Quantenmechanik
journal, July 1927
- Ehrenfest, P.
- Zeitschrift f�r Physik, Vol. 45, Issue 7-8
The emergence of gauge invariance: The stay-at-home gauge versus local–global duality
journal, April 2012
- Zaanen, J.; Beekman, A. J.
- Annals of Physics, Vol. 327, Issue 4
Commensurate 4 a 0 -period charge density modulations throughout the Bi 2 Sr 2 CaCu 2 O 8+x pseudogap regime
journal, October 2016
- Mesaros, Andrej; Fujita, Kazuhiro; Edkins, Stephen D.
- Proceedings of the National Academy of Sciences, Vol. 113, Issue 45
Scanning tunneling spectroscopy of high-temperature superconductors
journal, March 2007
- Fischer, Øystein; Kugler, Martin; Maggio-Aprile, Ivan
- Reviews of Modern Physics, Vol. 79, Issue 1
Redundancies in Nambu-Goldstone Bosons
journal, May 2013
- Watanabe, Haruki; Murayama, Hitoshi
- Physical Review Letters, Vol. 110, Issue 18
Confinement criterion for QCD with dynamical quarks
journal, January 1986
- Fredenhagen, Klaus; Marcu, Mihail
- Physical Review Letters, Vol. 56, Issue 3
Vortex Sublattice Melting in a Two-Component Superconductor
journal, March 2005
- Smørgrav, E.; Smiseth, J.; Babaev, E.
- Physical Review Letters, Vol. 94, Issue 9
Quantum lattice gas and the existence of a supersolid
journal, March 1973
- Liu, Kao-Shien; Fisher, Michael E.
- Journal of Low Temperature Physics, Vol. 10, Issue 5-6
Supersolid State of Matter
journal, April 2005
- Prokof’ev, Nikolay; Svistunov, Boris
- Physical Review Letters, Vol. 94, Issue 15
Continuum dual theory of the transition in 3D lattice superconductor
journal, January 1997
- Herbut, Igor F.
- Journal of Physics A: Mathematical and General, Vol. 30, Issue 2
Dislocation-mediated melting in two dimensions
journal, March 1979
- Nelson, David R.; Halperin, B. I.
- Physical Review B, Vol. 19, Issue 5
Angular Fluctuations of a Multicomponent Order Describe the Pseudogap of YBa2Cu3O6+x
journal, March 2014
- Hayward, L. E.; Hawthorn, D. G.; Melko, R. G.
- Science, Vol. 343, Issue 6177
Origin of the decrease in the torsional-oscillator period of solid
journal, July 2007
- Nussinov, Z.; Balatsky, A. V.; Graf, M. J.
- Physical Review B, Vol. 76, Issue 1
Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
journal, January 2015
- Kapfer, Sebastian C.; Krauth, Werner
- Physical Review Letters, Vol. 114, Issue 3
Electronic liquid-crystal phases of a doped Mott insulator
journal, June 1998
- Kivelson, S. A.; Fradkin, E.; Emery, V. J.
- Nature, Vol. 393, Issue 6685
Vortices in Multicomponent Bose–Einstein Condensates
journal, April 2005
- Kasamatsu, Kenichi; Tsubota, Makoto; Ueda, Masahito
- International Journal of Modern Physics B, Vol. 19, Issue 11
Hamiltonian formulation of Wilson's lattice gauge theories
journal, January 1975
- Kogut, John; Susskind, Leonard
- Physical Review D, Vol. 11, Issue 2
Electrical Resistivity Anisotropy from Self-Organized One Dimensionality in High-Temperature Superconductors
journal, March 2002
- Ando, Yoichi; Segawa, Kouji; Komiya, Seiki
- Physical Review Letters, Vol. 88, Issue 13
Antiferromagnetic order induced by an applied magnetic field in a high-temperature superconductor
journal, January 2002
- Lake, B.; Rønnow, H. M.; Christensen, N. B.
- Nature, Vol. 415, Issue 6869
Theory of Two-Dimensional Melting
journal, July 1978
- Halperin, B. I.; Nelson, David R.
- Physical Review Letters, Vol. 41, Issue 2
Statistics of the Two-Dimensional Ferromagnet. Part I
journal, August 1941
- Kramers, H. A.; Wannier, G. H.
- Physical Review, Vol. 60, Issue 3
Spontaneously Broken Spacetime Symmetries and Goldstone’s Theorem
journal, February 2002
- Low, Ian; Manohar, Aneesh V.
- Physical Review Letters, Vol. 88, Issue 10
Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
journal, January 1959
- Kröner, Ekkehart
- Archive for Rational Mechanics and Analysis, Vol. 4, Issue 1
Quantum magnetic excitations from stripes in copper oxide superconductors
journal, June 2004
- Tranquada, J. M.; Woo, H.; Perring, T. G.
- Nature, Vol. 429, Issue 6991
Off-Diagonal Long-Range Order in Solid
journal, March 2006
- Clark, Bryan K.; Ceperley, D. M.
- Physical Review Letters, Vol. 96, Issue 10
Duality in 2+1D quantum elasticity: superconductivity and quantum nematic order
journal, March 2004
- Zaanen, J.; Nussinov, Z.; Mukhin, S. I.
- Annals of Physics, Vol. 310, Issue 1
Mapping Noether identities into Bianchi identities in general relativistic theories of gravity and in the field theory of static lattice defects
journal, November 1990
- McCrea, J. Dermott; Hehl, Friedrich W.; Mielke, Eckehard W.
- International Journal of Theoretical Physics, Vol. 29, Issue 11
Kardar-Parisi-Zhang model and anomalous elasticity of two- and three-dimensional smectic- A liquid crystals
journal, April 1994
- Golubović, Leonardo; Wang, Zhen-Gang
- Physical Review E, Vol. 49, Issue 4
Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+δ
journal, January 2002
- Lang, K. M.; Madhavan, V.; Hoffman, J. E.
- Nature, Vol. 415, Issue 6870
Nematic world crystal model of gravity explaining absence of torsion in spacetime
journal, April 2004
- Kleinert, H.; Zaanen, J.
- Physics Letters A, Vol. 324, Issue 5-6
Quantum Liquid Crystals in an Imbalanced Fermi Gas: Fluctuations and Fractional Vortices in Larkin-Ovchinnikov States
journal, July 2009
- Radzihovsky, Leo; Vishwanath, Ashvin
- Physical Review Letters, Vol. 103, Issue 1
Example of a Negative Effective Poisson's Ratio
journal, September 1981
- Kittinger, E.; Tichý, J.; Bertagnolli, E.
- Physical Review Letters, Vol. 47, Issue 10
Liquid-crystal phases of quantum Hall systems
journal, March 1999
- Fradkin, Eduardo; Kivelson, Steven A.
- Physical Review B, Vol. 59, Issue 12
Monte Carlo study of two-step defect melting
journal, April 1990
- Janke, W.; Kleinert, H.
- Physical Review B, Vol. 41, Issue 10
Probable observation of a supersolid helium phase
journal, January 2004
- Kim, E.; Chan, M. H. W.
- Nature, Vol. 427, Issue 6971
Quantum-mechanical theory of stress and force
journal, September 1985
- Nielsen, O. H.; Martin, Richard M.
- Physical Review B, Vol. 32, Issue 6
Vortex duality: Observing the dual nature using order propagators
journal, October 2006
- Cvetkovic, V.; Zaanen, J.
- Physical Review B, Vol. 74, Issue 13
Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories
journal, September 2000
- Hove, J.; Mo, S.; Sudbø, A.
- Physical Review Letters, Vol. 85, Issue 11
Decoding Spatial Complexity in Strongly Correlated Electronic Systems
journal, January 2015
- Carlson, E. W.; Liu, Shuo; Phillabaum, B.
- Journal of Superconductivity and Novel Magnetism, Vol. 28, Issue 4
Colloquium : Supersolids: What and where are they?
journal, May 2012
- Boninsegni, Massimo; Prokof’ev, Nikolay V.
- Reviews of Modern Physics, Vol. 84, Issue 2
Stripe fractionalization I: The generation of king local symmetry
journal, November 2002
- Nussinov, Z.; Zaanen, J.
- Journal de Physique IV, Vol. 12, Issue 9
Works referencing / citing this record:
Elasticity bounds from effective field theory
journal, September 2019
- Alberte, Lasma; Baggioli, Matteo; Castillo, Víctor Cáncer
- Physical Review D, Vol. 100, Issue 6
Holography and hydrodynamics with weakly broken symmetries
journal, April 2019
- Grozdanov, Sašo; Lucas, Andrew; Poovuttikul, Napat
- Physical Review D, Vol. 99, Issue 8
Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography
text, January 2018
- Grozdanov, Sašo; Poovuttikul, Napat
- arXiv
Crystal-to-Fracton Tensor Gauge Theory Dualities
text, January 2019
- Pretko, Michael; Zhai, Zhengzheng; Radzihovsky, Leo
- arXiv
Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
text, January 2019
- Yan, Han
- arXiv
Fractonic line excitations: An inroad from three-dimensional elasticity theory
journal, June 2018
- Pai, Shriya; Pretko, Michael
- Physical Review B, Vol. 97, Issue 23
A unified description of translational symmetry breaking in holography
journal, September 2019
- Ammon, Martin; Baggioli, Matteo; Alba, Amadeo Jimenez
- Journal of High Energy Physics, Vol. 2019, Issue 9
Planckian dissipation, minimal viscosity and the transport in cuprate strange metals
journal, January 2019
- Zaanen, Jan
- SciPost Physics, Vol. 6, Issue 5
Charged black hole chemistry with massive gravitons
journal, December 2019
- Dehghani, Ali; Hendi, Seyed Hossein
- Classical and Quantum Gravity, Vol. 37, Issue 2
Spontaneous symmetry breaking in free theories with boundary potentials
journal, August 2021
- Prochazka, Vladimir; Söderberg, Alexander
- SciPost Physics, Vol. 11, Issue 2
Confinement of half-quantized vortices in coherently coupled Bose-Einstein condensates: Simulating quark confinement in a QCD-like theory
journal, February 2018
- Eto, Minoru; Nitta, Muneto
- Physical Review A, Vol. 97, Issue 2
Symmetry Enriched Fracton Phases from Supersolid Duality
text, January 2018
- Pretko, Michael; Radzihovsky, Leo
- arXiv
Zoology of Solid & Fluid Holography : Goldstone Modes and Phase Relaxation
text, January 2019
- Baggioli, Matteo; Grieninger, Sebastian
- arXiv
Dual gauge field theory of quantum liquid crystals in three dimensions
journal, October 2017
- Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai
- Physical Review B, Vol. 96, Issue 16
Charged and neutral fixed points in the model with Abelian gauge fields
journal, July 2019
- Beekman, Aron J.; Fejős, Gergely
- Physical Review D, Vol. 100, Issue 1
Quantum mechanism of condensation and high T c superconductivity
journal, June 2019
- Ma, Tian; Wang, Shouhong
- International Journal of Modern Physics B, Vol. 33, Issue 14
Simple views on symmetries and dualities in the theory of elasticity
text, January 2019
- Fruchart, Michel; Vitelli, Vincenzo
- arXiv
Chiral Topological Elasticity and Fracton Order
journal, February 2019
- Gromov, Andrey
- Physical Review Letters, Vol. 122, Issue 7
Generalized global symmetries in states with dynamical defects: The case of the transverse sound in field theory and holography
journal, May 2018
- Grozdanov, Sašo; Poovuttikul, Napat
- Physical Review D, Vol. 97, Issue 10
Charged black hole chemistry with massive gravitons
text, January 2019
- Dehghani, Ali; Hendi, Seyed Hossein
- arXiv
Holographic Phonons
journal, April 2018
- Alberte, Lasma; Ammon, Martin; Jiménez-Alba, Amadeo
- Physical Review Letters, Vol. 120, Issue 17
Dual gauge field theory of quantum liquid crystals in three dimensions
text, January 2017
- Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai
- arXiv