Odd fracton theories, proximate orders, and parton constructions

Pretko, Michael; Parameswaran, S. A.; Hermele, Michael

doi:10.1103/physrevb.102.205106

Title: Odd fracton theories, proximate orders, and parton constructions

Journal Article · Fri Nov 06 00:00:00 EST 2020 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.102.205106· OSTI ID:1762129

^[1];

^[2]; Hermele, Michael ^[1]

Univ. of Colorado, Boulder, CO (United States)
Clarendon Lab., Oxford (United Kingdom)

The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy nontrivial conditions on their low-energy properties when a combination of lattice translation and U(1) symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other subdimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that “odd” versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd Z₂ gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry breaking, thereby allowing us to identify a class of conventionally ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. In conclusion, condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); European Research Council (ERC)

Grant/Contract Number:: SC0014415; 804213-TMCS

OSTI ID:: 1762129

Journal Information:: Physical Review. B, Vol. 102, Issue 20; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (68)

A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations Vijay, Sagar; Haah, Jeongwan; Fu, Liang Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235136	journal	December 2015
Phase diagram of a frustrated quantum antiferromagnet on the honeycomb lattice: Magnetic order versus valence-bond crystal formation Albuquerque, A. F.; Schwandt, D.; Hetényi, B. Physical Review B, Vol. 84, Issue 2 https://doi.org/10.1103/PhysRevB.84.024406	journal	July 2011
Fractons from partons Hsieh, Timothy H.; Halász, Gábor B. Physical Review B, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevB.96.165105	journal	October 2017
Commuting Pauli Hamiltonians as Maps between Free Modules Haah, Jeongwan Communications in Mathematical Physics, Vol. 324, Issue 2 https://doi.org/10.1007/s00220-013-1810-2	journal	October 2013
Fractionalizing glide reflections in two-dimensional $Z_{2}$ topologically ordered phases Lee, SungBin; Hermele, Michael; Parameswaran, S. A. Physical Review B, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevB.94.125122	journal	September 2016
Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection Chamon, Claudio Physical Review Letters, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevLett.94.040402	journal	January 2005
Symmetry fractionalization in two dimensional topological phases Chen, Xie Reviews in Physics, Vol. 2 https://doi.org/10.1016/j.revip.2017.02.002	journal	November 2017
Quantum spin liquids: a review Savary, Lucile; Balents, Leon Reports on Progress in Physics, Vol. 80, Issue 1 https://doi.org/10.1088/0034-4885/80/1/016502	journal	November 2016
Quantum orders and symmetric spin liquids Wen, Xiao-Gang Physical Review B, Vol. 65, Issue 16 https://doi.org/10.1103/PhysRevB.65.165113	journal	April 2002
Planar ordering in the plaquette-only gonihedric Ising model Mueller, Marco; Janke, Wolfhard; Johnston, Desmond A. Nuclear Physics B, Vol. 894 https://doi.org/10.1016/j.nuclphysb.2015.02.020	journal	May 2015
Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model Moessner, R.; Sondhi, S. L. Physical Review Letters, Vol. 86, Issue 9 https://doi.org/10.1103/PhysRevLett.86.1881	journal	February 2001
Classification of symmetry enriched topological phases with exactly solvable models Mesaros, Andrej; Ran, Ying Physical Review B, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevB.87.155115	journal	April 2013
Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice Zhao, H. H.; Xu, Cenke; Chen, Q. N. Physical Review B, Vol. 85, Issue 13 https://doi.org/10.1103/PhysRevB.85.134416	journal	April 2012
Lieb-Schultz-Mattis–type constraints on fractonic matter He, Huan; You, Yizhi; Prem, Abhinav Physical Review B, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevB.101.165145	journal	April 2020
Weak Plaquette Valence Bond Order in the $S = 1 / 2$ Honeycomb $J_{1} - J_{2}$ Heisenberg Model Zhu, Zhenyue; Huse, David A.; White, Steven R. Physical Review Letters, Vol. 110, Issue 12 https://doi.org/10.1103/PhysRevLett.110.127205	journal	March 2013
Vacuum degeneracy of chiral spin states in compactified space Wen, X. G. Physical Review B, Vol. 40, Issue 10 https://doi.org/10.1103/PhysRevB.40.7387	journal	October 1989
Cage-Net Fracton Models Prem, Abhinav; Huang, Sheng-Jie; Song, Hao Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021010	journal	April 2019
Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory Ma, Han; Hermele, Michael; Chen, Xie Physical Review B, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevB.98.035111	journal	July 2018
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces Wen, X. G.; Niu, Q. Physical Review B, Vol. 41, Issue 13 https://doi.org/10.1103/PhysRevB.41.9377	journal	May 1990
Symmetric fracton matter: Twisted and enriched You, Yizhi; Devakul, Trithep; Burnell, F. J. Annals of Physics, Vol. 416 https://doi.org/10.1016/j.aop.2020.168140	journal	May 2020
Generalized electromagnetism of subdimensional particles: A spin liquid story Pretko, Michael Physical Review B, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevB.96.035119	journal	July 2017
Two soluble models of an antiferromagnetic chain Lieb, Elliott; Schultz, Theodore; Mattis, Daniel Annals of Physics, Vol. 16, Issue 3 https://doi.org/10.1016/0003-4916(61)90115-4	journal	December 1961
Fractonic matter in symmetry-enriched $U (1)$ gauge theory Williamson, Dominic J.; Bi, Zhen; Cheng, Meng Physical Review B, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevB.100.125150	journal	September 2019
Fracton topological order via coupled layers Ma, Han; Lake, Ethan; Chen, Xie Physical Review B, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevB.95.245126	journal	June 2017
Localization in Fractonic Random Circuits Pai, Shriya; Pretko, Michael; Nandkishore, Rahul M. Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021003	journal	April 2019
Fracton fusion and statistics Pai, Shriya; Hermele, Michael Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevB.100.195136	journal	November 2019
Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice Oshikawa, Masaki Physical Review Letters, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevLett.84.1535	journal	February 2000
Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance Hastings, M. B.; Wen, Xiao-Gang Physical Review B, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevB.72.045141	journal	July 2005
Fracton topological order, generalized lattice gauge theory, and duality Vijay, Sagar; Haah, Jeongwan; Fu, Liang Physical Review B, Vol. 94, Issue 23 https://doi.org/10.1103/PhysRevB.94.235157	journal	December 2016
Algebraic Methods for Quantum Codes on Lattices Haah, Jeongwan Revista Colombiana de Matemáticas, Vol. 50, Issue 2 https://doi.org/10.15446/recolma.v50n2.62214	journal	January 2017
Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters Wegner, Franz J. Journal of Mathematical Physics, Vol. 12, Issue 10 https://doi.org/10.1063/1.1665530	journal	October 1971
Symmetry fractionalization, defects, and gauging of topological phases Barkeshli, Maissam; Bonderson, Parsa; Cheng, Meng Physical Review B, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevB.100.115147	journal	September 2019
Higgs mechanism in higher-rank symmetric U(1) gauge theories Bulmash, Daniel; Barkeshli, Maissam Physical Review B, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevB.97.235112	journal	June 2018
Variational study of triangular lattice spin- $1 ∕ 2$ model with ring exchanges and spin liquid state in $κ − {(ET)}_{2} {Cu}_{2} {(CN)}_{3}$ Motrunich, Olexei I. Physical Review B, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevB.72.045105	journal	July 2005
Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories Moessner, R.; Sondhi, S. L.; Fradkin, Eduardo Physical Review B, Vol. 65, Issue 2 https://doi.org/10.1103/PhysRevB.65.024504	journal	December 2001
Spectroscopic signatures of crystal momentum fractionalization Essin, Andrew M.; Hermele, Michael Physical Review B, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevB.90.121102	journal	September 2014
Quantum robustness of fracton phases Mühlhauser, M.; Walther, M. R.; Reiss, D. A. Physical Review B, Vol. 101, Issue 5 https://doi.org/10.1103/PhysRevB.101.054426	journal	February 2020
Fracton Models on General Three-Dimensional Manifolds Shirley, Wilbur; Slagle, Kevin; Wang, Zhenghan Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031051	journal	August 2018
Anomalous Symmetry Fractionalization and Surface Topological Order Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041013	journal	October 2015
Rank–2 $U (1)$ Spin Liquid on the Breathing Pyrochlore Lattice Yan, Han; Benton, Owen; Jaubert, L. D. C. Physical Review Letters, Vol. 124, Issue 12 https://doi.org/10.1103/PhysRevLett.124.127203	journal	March 2020
Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice Gong, Shou-Shu; Zhu, Wei; Balents, Leon Physical Review B, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevB.91.075112	journal	February 2015
Emergent fractons and algebraic quantum liquid from plaquette melting transitions You, Yizhi; Bi, Zhen; Pretko, Michael Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/PhysRevResearch.2.013162	journal	February 2020
Topological Orders in Rigid States Wen, X. G. International Journal of Modern Physics B, Vol. 04, Issue 02 https://doi.org/10.1142/S0217979290000139	journal	February 1990
Subdimensional particle structure of higher rank $U (1)$ spin liquids Pretko, Michael Physical Review B, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevB.95.115139	journal	March 2017
Lieb-Schultz-Mattis in higher dimensions Hastings, M. B. Physical Review B, Vol. 69, Issue 10 https://doi.org/10.1103/PhysRevB.69.104431	journal	March 2004
Deconfined quantum criticality and Néel order via dimer disorder Levin, Michael; Senthil, T. Physical Review B, Vol. 70, Issue 22 https://doi.org/10.1103/PhysRevB.70.220403	journal	December 2004
Symmetry-Enriched Fracton Phases from Supersolid Duality Pretko, Michael; Radzihovsky, Leo Physical Review Letters, Vol. 121, Issue 23 https://doi.org/10.1103/PhysRevLett.121.235301	journal	December 2018
Sufficient conditions for topological order in insulators Hastings, M. B. Europhysics Letters (EPL), Vol. 70, Issue 6 https://doi.org/10.1209/epl/i2005-10046-x	journal	June 2005
Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field Moessner, R.; Sondhi, S. L.; Chandra, P. Physical Review Letters, Vol. 84, Issue 19 https://doi.org/10.1103/PhysRevLett.84.4457	journal	May 2000
Fracton phases of matter Pretko, Michael; Chen, Xie; You, Yizhi International Journal of Modern Physics A, Vol. 35, Issue 06 https://doi.org/10.1142/S0217751X20300033	journal	February 2020
Fractons Nandkishore, Rahul M.; Hermele, Michael Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031218-013604	journal	March 2019
Plaquette Ordered Phase and Quantum Phase Diagram in the Spin- $\frac{1}{2}$ $J_{1} − J_{2}$ Square Heisenberg Model Gong, Shou-Shu; Zhu, Wei; Sheng, D. N. Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.027201	journal	July 2014
Resonating plaquette phases in SU(4) Heisenberg antiferromagnet Xu, Cenke; Wu, Congjun Physical Review B, Vol. 77, Issue 13 https://doi.org/10.1103/PhysRevB.77.134449	journal	April 2008
Chiral Topological Elasticity and Fracton Order Gromov, Andrey Physical Review Letters, Vol. 122, Issue 7 https://doi.org/10.1103/PhysRevLett.122.076403	journal	February 2019
Hyperbolic fracton model, subsystem symmetry, and holography Yan, Han Physical Review B, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevB.99.155126	journal	April 2019
U(1) Gauge Theory of the Hubbard Model: Spin Liquid States and Possible Application to $κ − (BEDT − TTF)_{2} {Cu}_{2} (CN)_{3}$ Lee, Sung-Sik; Lee, Patrick A. Physical Review Letters, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevLett.95.036403	journal	July 2005
Symmetry-enforced fractonicity and two-dimensional quantum crystal melting Kumar, Ajesh; Potter, Andrew C. Physical Review B, Vol. 100, Issue 4 https://doi.org/10.1103/physrevb.100.045119	journal	July 2019
Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory Blankschtein, Daniel; Ma, M.; Berker, A. Nihat Physical Review B, Vol. 30, Issue 3 https://doi.org/10.1103/physrevb.30.1362	journal	August 1984
Extending Luttinger’s theorem to $Z_{2}$ fractionalized phases of matter Paramekanti, Arun; Vishwanath, Ashvin Physical Review B, Vol. 70, Issue 24 https://doi.org/10.1103/physrevb.70.245118	journal	December 2004
Resonating singlet valence plaquettes Pankov, S.; Moessner, R.; Sondhi, S. L. Physical Review B, Vol. 76, Issue 10 https://doi.org/10.1103/physrevb.76.104436	journal	September 2007
Spectroscopic signatures of crystal momentum fractionalization Essin, Andrew M.; Hermele, Michael arXiv https://doi.org/10.48550/arxiv.1401.1846	text	January 2014
A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations Vijay, Sagar; Haah, Jeongwan; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1505.02576	text	January 2015
Quantum Spin Liquids Savary, Lucile; Balents, Leon arXiv https://doi.org/10.48550/arxiv.1601.03742	text	January 2016
Fracton Topological Order, Generalized Lattice Gauge Theory and Duality Vijay, Sagar; Haah, Jeongwan; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1603.04442	text	January 2016
Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story Pretko, Michael arXiv https://doi.org/10.48550/arxiv.1606.08857	text	January 2016
Fracton Phases of Matter Pretko, Michael; Chen, Xie; You, Yizhi arXiv https://doi.org/10.48550/arxiv.2001.01722	text	January 2020
Local stabilizer codes in three dimensions without string logical operators Haah, Jeongwan University of Southern California (USC) https://doi.org/10.5446/35310	audiovisual	January 2011
Emergent fractons and algebraic quantum liquid from plaquette melting transitions You, Yizhi Banff International Research Station for Mathematical Innovation and Discovery https://doi.org/10.14288/1.0392552	audiovisual	January 2020

Cited By (1)

(Four) Dual Plaquette 3D Ising Models Johnston, Desmond A.; Ranasinghe, R. P. K. C. M. arXiv https://doi.org/10.48550/arxiv.2006.05377	text	January 2020

Similar Records

Fracton fusion and statistics

Journal Article · Fri Nov 22 00:00:00 EST 2019 · Physical Review. B · OSTI ID:1762129

Pai, Shriya; Hermele, Michael

Subdimensional criticality: Condensation of lineons and planons in the X-cube model

Journal Article · Mon Oct 11 00:00:00 EDT 2021 · Physical Review. B · OSTI ID:1762129

Lake, Ethan; Hermele, Michael

Fractons from Vector Gauge Theory

Journal Article · Fri Feb 07 00:00:00 EST 2020 · Physical Review Letters · OSTI ID:1762129

Radzihovsky, Leo; Hermele, Michael

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Fractionalization
Gauge theories
Symmetry protected topological states
Topological phases of matter

Title: Odd fracton theories, proximate orders, and parton constructions

Citation Formats

References (68)

Cited By (1)

Similar Records

Related Subjects