Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays
Abstract
In this work, we describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.
- Authors:
-
- Harvard Univ., Cambridge, MA (United States)
- Harvard Univ., Cambridge, MA (United States); Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- Harvard Univ., Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); Gordon and Betty Moore Foundation
- OSTI Identifier:
- 1803508
- Alternate Identifier(s):
- OSTI ID: 1603837
- Grant/Contract Number:
- SC0019030; GBMF4306; AY2019/2020; GBMF8682
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 124; Journal Issue: 10; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; Physics
Citation Formats
Samajdar, Rhine, Ho, Wen Wei, Pichler, Hannes, Lukin, Mikhail D., and Sachdev, Subir. Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays. United States: N. p., 2020.
Web. doi:10.1103/physrevlett.124.103601.
Samajdar, Rhine, Ho, Wen Wei, Pichler, Hannes, Lukin, Mikhail D., & Sachdev, Subir. Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays. United States. https://doi.org/10.1103/physrevlett.124.103601
Samajdar, Rhine, Ho, Wen Wei, Pichler, Hannes, Lukin, Mikhail D., and Sachdev, Subir. Tue .
"Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays". United States. https://doi.org/10.1103/physrevlett.124.103601. https://www.osti.gov/servlets/purl/1803508.
@article{osti_1803508,
title = {Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays},
author = {Samajdar, Rhine and Ho, Wen Wei and Pichler, Hannes and Lukin, Mikhail D. and Sachdev, Subir},
abstractNote = {In this work, we describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.},
doi = {10.1103/physrevlett.124.103601},
journal = {Physical Review Letters},
number = 10,
volume = 124,
place = {United States},
year = {Tue Mar 10 00:00:00 EDT 2020},
month = {Tue Mar 10 00:00:00 EDT 2020}
}
Web of Science
Works referenced in this record:
Sorting ultracold atoms in a three-dimensional optical lattice in a realization of Maxwell’s demon
journal, September 2018
- Kumar, Aishwarya; Wu, Tsung-Yao; Giraldo, Felipe
- Nature, Vol. 561, Issue 7721
Two-dimensional packing problems: A survey
journal, September 2002
- Lodi, Andrea; Martello, Silvano; Monaci, Michele
- European Journal of Operational Research, Vol. 141, Issue 2
Trapped-ion quantum computing: Progress and challenges
journal, June 2019
- Bruzewicz, Colin D.; Chiaverini, John; McConnell, Robert
- Applied Physics Reviews, Vol. 6, Issue 2
Gradient optimization of finite projected entangled pair states
journal, May 2017
- Liu, Wen-Yuan; Dong, Shao-Jun; Han, Yong-Jian
- Physical Review B, Vol. 95, Issue 19
Phase Separation in Supersolids
journal, February 2000
- Batrouni, G. G.; Scalettar, R. T.
- Physical Review Letters, Vol. 84, Issue 7
Physical Realizations of Vector Models
journal, February 1975
- Mukamel, David
- Physical Review Letters, Vol. 34, Issue 8
Many-body physics with ultracold gases
journal, July 2008
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- Reviews of Modern Physics, Vol. 80, Issue 3
Two-dimensional Rydberg Gases and the Quantum Hard-Squares Model
journal, August 2011
- Ji, S.; Ates, C.; Lesanovsky, I.
- Physical Review Letters, Vol. 107, Issue 6
A measure of data collapse for scaling
journal, August 2001
- Bhattacharjee, Somendra M.; Seno, Flavio
- Journal of Physics A: Mathematical and General, Vol. 34, Issue 33
Critical exponents for a three-dimensional O( n )-symmetric model with n >3
journal, March 1995
- Antonenko, S. A.; Sokolov, A. I.
- Physical Review E, Vol. 51, Issue 3
Critical Exponents of the Quantum Phase Transition in a Planar Antiferromagnet
journal, October 1997
- Troyer, Matthias; Imada, Masatoshi; Ueda, Kazuo
- Journal of the Physical Society of Japan, Vol. 66, Issue 10
Dependence of Critical Properties on Dimensionality of Spins
journal, March 1968
- Stanley, H. E.
- Physical Review Letters, Vol. 20, Issue 12
Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions
journal, March 1980
- Binder, K.; Landau, D. P.
- Physical Review B, Vol. 21, Issue 5
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
Hard-Core Bosons on a Two-Dimensional Square Optical Superlattice
journal, March 2015
- Li, Xiao-Juan; Wen, Yu-Chuan
- Communications in Theoretical Physics, Vol. 63, Issue 3
Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions
journal, June 2018
- Lienhard, Vincent; de Léséleuc, Sylvain; Barredo, Daniel
- Physical Review X, Vol. 8, Issue 2
Probing many-body dynamics on a 51-atom quantum simulator
journal, November 2017
- Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander
- Nature, Vol. 551, Issue 7682
Coherent and dissipative dynamics of entangled few-body systems of Rydberg atoms
journal, April 2019
- Lee, Woojun; Kim, Minhyuk; Jo, Hanlae
- Physical Review A, Vol. 99, Issue 4
Cosmological experiments in superfluid helium?
journal, October 1985
- Zurek, W. H.
- Nature, Vol. 317, Issue 6037
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014
- El-Showk, Sheer; Paulos, Miguel F.; Poland, David
- Journal of Statistical Physics, Vol. 157, Issue 4-5
Phases of lattice hard-core bosons in a periodic superlattice
journal, June 2010
- Dang, Long; Boninsegni, Massimo
- Physical Review B, Vol. 81, Issue 22
Quantum phases of strongly interacting Rydberg atoms in triangular lattices
journal, June 2013
- Qian, Jing; Zhou, Lu; Zhang, Weiping
- Physical Review A, Vol. 87, Issue 6
Interacting N-vector order parameters with O(N) symmetry
journal, January 2005
- Pelissetto, A.; Vicari, E.
- Condensed Matter Physics, Vol. 8, Issue 1
Dynamical Crystallization in the Dipole Blockade of Ultracold Atoms
journal, January 2010
- Pohl, T.; Demler, E.; Lukin, M. D.
- Physical Review Letters, Vol. 104, Issue 4
Vison states and confinement transitions of spin liquids on the kagome lattice
journal, September 2011
- Huh, Yejin; Punk, Matthias; Sachdev, Subir
- Physical Review B, Vol. 84, Issue 9
High-Fidelity Control and Entanglement of Rydberg-Atom Qubits
journal, September 2018
- Levine, Harry; Keesling, Alexander; Omran, Ahmed
- Physical Review Letters, Vol. 121, Issue 12
Precision islands in the Ising and O(N ) models
journal, August 2016
- Kos, Filip; Poland, David; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2016, Issue 8
Quantum phases of hardcore bosons with long-range interactions on a square lattice
journal, August 2012
- Yamamoto, Daisuke; Masaki, Akiko; Danshita, Ippei
- Physical Review B, Vol. 86, Issue 5
The density-matrix renormalization group
journal, April 2005
- Schollwöck, U.
- Reviews of Modern Physics, Vol. 77, Issue 1
Vacancy supersolid of hard-core bosons on the square lattice
journal, October 2008
- Dang, Long; Boninsegni, Massimo; Pollet, Lode
- Physical Review B, Vol. 78, Issue 13
Defect-Free Assembly of 2D Clusters of More Than 100 Single-Atom Quantum Systems
journal, May 2019
- Ohl de Mello, Daniel; Schäffner, Dominik; Werkmann, Jan
- Physical Review Letters, Vol. 122, Issue 20
Critical phenomena and renormalization-group theory
journal, October 2002
- Pelissetto, Andrea; Vicari, Ettore
- Physics Reports, Vol. 368, Issue 6
A Lattice Model of Liquid Helium, I
journal, December 1956
- Matsubara, Takeo; Matsuda, Hirotsugu
- Progress of Theoretical Physics, Vol. 16, Issue 6
gauge theory for valence bond solids on the kagome lattice
journal, November 2015
- Hwang, Kyusung; Huh, Yejin; Kim, Yong Baek
- Physical Review B, Vol. 92, Issue 20
Application of the renormalization group to phase transitions in disordered systems
journal, February 1976
- Grinstein, G.; Luther, A.
- Physical Review B, Vol. 13, Issue 3
Topology of cosmic domains and strings
journal, August 1976
- Kibble, T. W. B.
- Journal of Physics A: Mathematical and General, Vol. 9, Issue 8
Anisotropic perturbations in three-dimensional O( )-symmetric vector models
journal, September 2011
- Hasenbusch, Martin; Vicari, Ettore
- Physical Review B, Vol. 84, Issue 12
Coherent Many-Body Spin Dynamics in a Long-Range Interacting Ising Chain
journal, December 2017
- Zeiher, Johannes; Choi, Jae-yoon; Rubio-Abadal, Antonio
- Physical Review X, Vol. 7, Issue 4
Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets
journal, December 2015
- Qin, Yan Qi; Normand, B.; Sandvik, Anders W.
- Physical Review B, Vol. 92, Issue 21
Fast Quantum Gates for Neutral Atoms
journal, September 2000
- Jaksch, D.; Cirac, J. I.; Zoller, P.
- Physical Review Letters, Vol. 85, Issue 10
Weak ergodicity breaking from quantum many-body scars
journal, May 2018
- Turner, C. J.; Michailidis, A. A.; Abanin, D. A.
- Nature Physics, Vol. 14, Issue 7
Some implications of a cosmological phase transition
journal, December 1980
- Kibble, T. W. B.
- Physics Reports, Vol. 67, Issue 1
Synthetic three-dimensional atomic structures assembled atom by atom
journal, September 2018
- Barredo, Daniel; Lienhard, Vincent; de Léséleuc, Sylvain
- Nature, Vol. 561, Issue 7721
Defect-free atomic array formation using the Hungarian matching algorithm
journal, May 2017
- Lee, Woojun; Kim, Hyosub; Ahn, Jaewook
- Physical Review A, Vol. 95, Issue 5
Scaling Theory for Finite-Size Effects in the Critical Region
journal, June 1972
- Fisher, Michael E.; Barber, Michael N.
- Physical Review Letters, Vol. 28, Issue 23
Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions
journal, May 1999
- Hasenbusch, M.; Pinn, K.; Vinti, S.
- Physical Review B, Vol. 59, Issue 17
Numerical study of the chiral quantum phase transition in one spatial dimension
journal, August 2018
- Samajdar, Rhine; Choi, Soonwon; Pichler, Hannes
- Physical Review A, Vol. 98, Issue 2
Two-dimensional crystals of Rydberg excitations in a resonantly driven lattice gas
journal, October 2013
- Petrosyan, David
- Physical Review A, Vol. 88, Issue 4
Cosmological experiments in condensed matter systems
journal, November 1996
- Zurek, W. H.
- Physics Reports, Vol. 276, Issue 4
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
journal, March 2012
- Stoudenmire, E. M.; White, Steven R.
- Annual Review of Condensed Matter Physics, Vol. 3, Issue 1
A Rydberg quantum simulator
journal, March 2010
- Weimer, Hendrik; Müller, Markus; Lesanovsky, Igor
- Nature Physics, Vol. 6, Issue 5
Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet
journal, April 2011
- Yan, S.; Huse, D. A.; White, S. R.
- Science, Vol. 332, Issue 6034
epsilon -expansion analysis of some physically realizable n⩾4 vector models
journal, November 1975
- Mukamel, D.; Krinsky, S.
- Journal of Physics C: Solid State Physics, Vol. 8, Issue 22
Creation of collective many-body states and single photons from two-dimensional Rydberg lattice gases
journal, September 2011
- Laycock, T.; Olmos, B.; Lesanovsky, I.
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 44, Issue 18
Density-matrix algorithms for quantum renormalization groups
journal, October 1993
- White, Steven R.
- Physical Review B, Vol. 48, Issue 14
Renormalization-group analysis of chiral transitions
journal, September 1988
- Kawamura, Hikaru
- Physical Review B, Vol. 38, Issue 7
Neél Order in Square and Triangular Lattice Heisenberg Models
journal, September 2007
- White, Steven R.; Chernyshev, A. L.
- Physical Review Letters, Vol. 99, Issue 12
Quantum phase transitions in the two-dimensional hardcore boson model
journal, December 2001
- Hébert, F.; Batrouni, G. G.; Scalettar, R. T.
- Physical Review B, Vol. 65, Issue 1
Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field
journal, November 2011
- Graß, T.; Saha, K.; Sengupta, K.
- Physical Review A, Vol. 84, Issue 5
Quantum field theory for the chiral clock transition in one spatial dimension
journal, November 2018
- Whitsitt, Seth; Samajdar, Rhine; Sachdev, Subir
- Physical Review B, Vol. 98, Issue 20
Mott insulators in strong electric fields
journal, August 2002
- Sachdev, Subir; Sengupta, K.; Girvin, S. M.
- Physical Review B, Vol. 66, Issue 7
Scaling and Renormalization in Statistical Physics
book, January 2015
- Cardy, John
- Cambridge University Press
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models
journal, June 2016
- Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain
- Nature, Vol. 534, Issue 7609
Putting competing orders in their place near the Mott transition
journal, April 2005
- Balents, Leon; Bartosch, Lorenz; Burkov, Anton
- Physical Review B, Vol. 71, Issue 14
Finite-size behavior of the Ising square lattice
journal, April 1976
- Landau, D. P.
- Physical Review B, Vol. 13, Issue 7
Atom-by-atom assembly of defect-free one-dimensional cold atom arrays
journal, November 2016
- Endres, Manuel; Bernien, Hannes; Keesling, Alexander
- Science, Vol. 354, Issue 6315
Observation of spatially ordered structures in a two-dimensional Rydberg gas
journal, October 2012
- Schauß, Peter; Cheneau, Marc; Endres, Manuel
- Nature, Vol. 491, Issue 7422
A coherent quantum annealer with Rydberg atoms
journal, June 2017
- Glaetzle, A. W.; van Bijnen, R. M. W.; Zoller, P.
- Nature Communications, Vol. 8, Issue 1
Competing density-wave orders in a one-dimensional hard-boson model
journal, February 2004
- Fendley, Paul; Sengupta, K.; Sachdev, Subir
- Physical Review B, Vol. 69, Issue 7
The density-matrix renormalization group: a short introduction
journal, July 2011
- Schollwöck, Ulrich
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, Issue 1946
-vector spin models on the simple-cubic and the body-centered-cubic lattices: A study of the critical behavior of the susceptibility and of the correlation length by high-temperature series extended to order
journal, October 1997
- Butera, P.; Comi, M.
- Physical Review B, Vol. 56, Issue 13
Gray-Molasses Optical-Tweezer Loading: Controlling Collisions for Scaling Atom-Array Assembly
journal, March 2019
- Brown, M. O.; Thiele, T.; Kiehl, C.
- Physical Review X, Vol. 9, Issue 1
The density-matrix renormalization group in the age of matrix product states
journal, January 2011
- Schollwöck, Ulrich
- Annals of Physics, Vol. 326, Issue 1
Finite-size scaling in the transverse Ising model on a square lattice
journal, September 2000
- Hamer, C. J.
- Journal of Physics A: Mathematical and General, Vol. 33, Issue 38
Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms
journal, August 2019
- de Léséleuc, Sylvain; Lienhard, Vincent; Scholl, Pascal
- Science, Vol. 365, Issue 6455
Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective
journal, April 1994
- Liang, Shoudan; Pang, Hanbin
- Physical Review B, Vol. 49, Issue 13
From coherent collective excitation to Rydberg blockade on an atom chip
journal, December 2018
- de Hond, Julius; van Bijnen, Rick; Kokkelmans, S. J. J. M. F.
- Physical Review A, Vol. 98, Issue 6
Supersolidity from defect condensation in the extended boson Hubbard model
journal, January 2008
- Chen, Yu-Chun; Melko, Roger G.; Wessel, Stefan
- Physical Review B, Vol. 77, Issue 1
Assembling Fibonacci anyons from a parafermion lattice model
journal, June 2015
- Stoudenmire, E. M.; Clarke, David J.; Mong, Roger S. K.
- Physical Review B, Vol. 91, Issue 23
Physical realizations of -component vector models. I. Derivation of the Landau-Ginzburg-Wilson Hamiltonians
journal, June 1976
- Mukamel, D.; Krinsky, S.
- Physical Review B, Vol. 13, Issue 11
Critical behavior of symmetric models
journal, November 2004
- Calabrese, Pasquale; Parruccini, Pietro; Pelissetto, Andrea
- Physical Review B, Vol. 70, Issue 17
Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator
journal, April 2019
- Keesling, Alexander; Omran, Ahmed; Levine, Harry
- Nature, Vol. 568, Issue 7751
From density-matrix renormalization group to matrix product states
journal, October 2007
- McCulloch, Ian P.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 10
Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
journal, August 2019
- Omran, A.; Levine, H.; Keesling, A.
- Science, Vol. 365, Issue 6453
Finite-size scaling in Hamiltonian field theory
journal, May 1980
- Hamer, C. J.; Barber, M. N.
- Journal of Physics A: Mathematical and General, Vol. 13, Issue 5
An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays
journal, November 2016
- Barredo, Daniel; de Léséleuc, Sylvain; Lienhard, Vincent
- Science, Vol. 354, Issue 6315
Finite size scaling analysis of ising model block distribution functions
journal, June 1981
- Binder, K.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 43, Issue 2
Density matrix renormalization group algorithms with a single center site
journal, November 2005
- White, Steven R.
- Physical Review B, Vol. 72, Issue 18
Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach
journal, January 2019
- Ho, Wen Wei; Choi, Soonwon; Pichler, Hannes
- Physical Review Letters, Vol. 122, Issue 4
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008
- Verstraete, F.; Murg, V.; Cirac, J. I.
- Advances in Physics, Vol. 57, Issue 2
Quantum information processing with superconducting circuits: a review
journal, September 2017
- Wendin, G.
- Reports on Progress in Physics, Vol. 80, Issue 10
Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet
journal, November 2014
- Robinson, Neil J.; Essler, Fabian H. L.; Cabrera, Ivelisse
- Physical Review B, Vol. 90, Issue 17
Analytical and numerical study of hardcore bosons in two dimensions
journal, February 2002
- Bernardet, K.; Batrouni, G. G.; Meunier, J. -L.
- Physical Review B, Vol. 65, Issue 10
Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
text, January 2014
- El-Showk, Sheer; Paulos, Miguel F.; Poland, David
- arXiv
Works referencing / citing this record:
Quantum phases of Rydberg atoms on a kagome lattice
text, January 2020
- Samajdar, Rhine; Ho, Wen Wei; Pichler, Hannes
- arXiv
Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
text, January 2020
- Scholl, Pascal; Schuler, Michael; Williams, Hannah J.
- arXiv