Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays

Slagle, Kevin; Liu, Yue; Aasen, David; Pichler, Hannes; Mong, Roger K.; Chen, Xie; Endres, Manuel; Alicea, Jason

doi:10.1103/physrevb.106.115122

Title: Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays

Journal Article · Wed Sep 14 00:00:00 EDT 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.106.115122· OSTI ID:1982786

^[1];

^[2]; Aasen, David ^[3]; Pichler, Hannes ^[4]; Mong, Roger K. ^[5]; Chen, Xie ^[2]; Endres, Manuel ^[2]; Alicea, Jason ^[2]

Rice Univ., Houston, TX (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)
Univ. of California, Santa Barbara, CA (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. Innsbruck (Austria); Austrian Academy of Sciences, Innsbruck (Austria)
Univ. of Pittsburgh, PA (United States)

Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model—albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z₂ spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing Floquet-mediated chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state “Kitaev materials” and, more generally, it spotlights a different angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.

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Research Organization:: National Quantum Information Science (QIS) Research Centers (United States). The Quantum Science Center (QSC)

Sponsoring Organization:: USDOE Office of Science (SC); US Army Research Office (ARO); National Science Foundation (NSF); Gordon and Betty Moore Foundation; US Air Force Office of Scientific Research (AFOSR); Defense Advanced Research Projects Agency (DARPA)

Grant/Contract Number:: AC05-00OR22725; W911NF-17-1-0323; DMR-1848336; GBMF1250; GBMF8682; FA9550-19-1-0044; OMA-2016245; W911NF2010021; 7568717

OSTI ID:: 1982786

Journal Information:: Physical Review. B, Vol. 106, Issue 11; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (78)

Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields Goldman, N.; Dalibard, J. Physical Review X, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevX.4.031027	journal	August 2014
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains Huang, Po-Hao; Chen, Jyong-Hao; Gomes, Pedro R. S. Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205123	journal	May 2016
Ordered phases of the anisotropic kagome-lattice antiferromagnet in a magnetic field Stoudenmire, E. M.; Balents, Leon Physical Review B, Vol. 77, Issue 17 https://doi.org/10.1103/PhysRevB.77.174414	journal	May 2008
Coupled-wire constructions: a Luttinger liquid approach to topology Meng, Tobias The European Physical Journal Special Topics, Vol. 229, Issue 4 https://doi.org/10.1140/epjst/e2019-900095-5	journal	February 2020
Coupled wire model of $Z_{4}$ orbifold quantum Hall states Kane, Charles L.; Stern, Ady Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085302	journal	August 2018
Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions Leviatan, Eyal; Mross, David F. Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043437	journal	December 2020
Time-Domain Anyon Interferometry in Kitaev Honeycomb Spin Liquids and Beyond Klocke, Kai; Aasen, David; Mong, Roger S. K. Physical Review Letters, Vol. 126, Issue 17 https://doi.org/10.1103/PhysRevLett.126.177204	journal	April 2021
Probing topological spin liquids on a programmable quantum simulator Semeghini, G.; Levine, H.; Keesling, A. Science, Vol. 374, Issue 6572 https://doi.org/10.1126/science.abi8794	journal	December 2021
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 phases of matter on a 256-atom programmable quantum simulator Ebadi, Sepehr; Wang, Tout T.; Levine, Harry Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03582-4	journal	July 2021
Intrinsic sign problem in fermionic and bosonic chiral topological matter Golan, Omri; Smith, Adam; Ringel, Zohar Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043032	journal	October 2020
Quantum Hall hierarchy from coupled wires Fuji, Yohei; Furusaki, Akira Physical Review B, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevB.99.035130	journal	January 2019
Quantum spin liquid states Zhou, Yi; Kanoda, Kazushi; Ng, Tai-Kai Reviews of Modern Physics, Vol. 89, Issue 2 https://doi.org/10.1103/RevModPhys.89.025003	journal	April 2017
Models and materials for generalized Kitaev magnetism Winter, Stephen M.; Tsirlin, Alexander A.; Daghofer, Maria Journal of Physics: Condensed Matter, Vol. 29, Issue 49 https://doi.org/10.1088/1361-648X/aa8cf5	journal	November 2017
Lattice spin models for non-Abelian chiral spin liquids Lecheminant, P.; Tsvelik, A. M. Physical Review B, Vol. 95, Issue 14 https://doi.org/10.1103/PhysRevB.95.140406	journal	April 2017
Intrinsic sign problems in topological quantum field theories Smith, Adam; Golan, Omri; Ringel, Zohar Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033515	journal	September 2020
Fractional topological phases in three-dimensional coupled-wire systems Meng, Tobias Physical Review B, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevB.92.115152	journal	September 2015
Theory of a 3+1D fractional chiral metal: Interacting variant of the Weyl semimetal Meng, Tobias; Grushin, Adolfo G.; Shtengel, Kirill Physical Review B, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevB.94.155136	journal	October 2016
Ordering in Spatially Anisotropic Triangular Antiferromagnets Starykh, Oleg A.; Balents, Leon Physical Review Letters, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevLett.98.077205	journal	February 2007
Ground-state degeneracy of non-Abelian topological phases from coupled wires Iadecola, Thomas; Neupert, Titus; Chamon, Claudio Physical Review B, Vol. 99, Issue 24 https://doi.org/10.1103/PhysRevB.99.245138	journal	June 2019
Chiral spin liquids in arrays of spin chains Gorohovsky, Gregory; Pereira, Rodrigo G.; Sela, Eran Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.245139	journal	June 2015
Prediction of Toric Code Topological Order from Rydberg Blockade Verresen, Ruben; Lukin, Mikhail D.; Vishwanath, Ashvin Physical Review X, Vol. 11, Issue 3 https://doi.org/10.1103/PhysRevX.11.031005	journal	July 2021
Electrically Detected Interferometry of Majorana Fermions in a Topological Insulator Akhmerov, A. R.; Nilsson, Johan; Beenakker, C. W. J. Physical Review Letters, Vol. 102, Issue 21 https://doi.org/10.1103/PhysRevLett.102.216404	journal	May 2009
Composite Weyl semimetal as a parent state for three-dimensional topologically ordered phases Sagi, Eran; Stern, Ady; Mross, David F. Physical Review B, Vol. 98, Issue 20 https://doi.org/10.1103/PhysRevB.98.201111	journal	November 2018
Topological order in 1D Cluster state protected by symmetry Son, W.; Amico, L.; Vedral, V. Quantum Information Processing, Vol. 11, Issue 6 https://doi.org/10.1007/s11128-011-0346-7	journal	December 2011
Time reversal symmetry broken fractional topological phases at zero magnetic field Meng, Tobias; Sela, Eran Physical Review B, Vol. 90, Issue 23 https://doi.org/10.1103/PhysRevB.90.235425	journal	December 2014
Coupled spin- $\frac{1}{2}$ ladders as microscopic models for non-Abelian chiral spin liquids Huang, Po-Hao; Chen, Jyong-Hao; Feiguin, Adrian E. Physical Review B, Vol. 95, Issue 14 https://doi.org/10.1103/PhysRevB.95.144413	journal	April 2017
Fractional chiral superconductors Sagi, Eran; Haim, Arbel; Berg, Erez Physical Review B, Vol. 96, Issue 23 https://doi.org/10.1103/PhysRevB.96.235144	journal	December 2017
Topological Order with a Twist: Ising Anyons from an Abelian Model Bombin, H. Physical Review Letters, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevLett.105.030403	journal	July 2010
Competing density-wave orders in a one-dimensional hard-boson model Fendley, Paul; Sengupta, K.; Sachdev, Subir Physical Review B, Vol. 69, Issue 7 https://doi.org/10.1103/PhysRevB.69.075106	journal	February 2004
Topologically protected quantum state transfer in a chiral spin liquid Yao, N. Y.; Laumann, C. R.; Gorshkov, A. V. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2531	journal	March 2013
Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order Mross, David F.; Essin, Andrew; Alicea, Jason Physical Review X, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevX.5.011011	journal	February 2015
Many-body physics with individually controlled Rydberg atoms Browaeys, Antoine; Lahaye, Thierry Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0733-z	journal	January 2020
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure Mong, Roger S. K.; Clarke, David J.; Alicea, Jason Physical Review X, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevX.4.011036	journal	March 2014
Fractional topological superconductivity and parafermion corner states Laubscher, Katharina; Loss, Daniel; Klinovaja, Jelena Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/PhysRevResearch.1.032017	journal	November 2019
Probing many-body dynamics on a 51-atom quantum simulator Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander Nature, Vol. 551, Issue 7682 https://doi.org/10.1038/nature24622	journal	November 2017
Quantum spin Hall effect in strip of stripes model Klinovaja, Jelena; Tserkovnyak, Yaroslav Physical Review B, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevB.90.115426	journal	September 2014
Pairing in Luttinger Liquids and Quantum Hall States Kane, Charles L.; Stern, Ady; Halperin, Bertrand I. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031009	journal	July 2017
Probing Neutral Majorana Fermion Edge Modes with Charge Transport Fu, Liang; Kane, C. L. Physical Review Letters, Vol. 102, Issue 21 https://doi.org/10.1103/PhysRevLett.102.216403	journal	May 2009
Fractional topological insulators: From sliding Luttinger liquids to Chern-Simons theory Santos, Raul A.; Huang, Chia-Wei; Gefen, Yuval Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/PhysRevB.91.205141	journal	May 2015
From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics Imamura, Yukihisa; Totsuka, Keisuke; Hansson, T. H. Physical Review B, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevB.100.125148	journal	September 2019
Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms de Léséleuc, Sylvain; Lienhard, Vincent; Scholl, Pascal Science, Vol. 365, Issue 6455 https://doi.org/10.1126/science.aav9105	journal	August 2019
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
Concept and realization of Kitaev quantum spin liquids Takagi, Hidenori; Takayama, Tomohiro; Jackeli, George Nature Reviews Physics, Vol. 1, Issue 4 https://doi.org/10.1038/s42254-019-0038-2	journal	March 2019
One-dimensional symmetry protected topological phases and their transitions Verresen, Ruben; Moessner, Roderich; Pollmann, Frank Physical Review B, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevB.96.165124	journal	October 2017
Coupled wire model of Z2×Z2 orbifold quantum Hall states Tam, Pok Man; Hu, Yichen; Kane, Charles L. Physical Review B, Vol. 101, Issue 12 https://doi.org/10.1103/PhysRevB.101.125104	journal	March 2020
Wire constructions of Abelian topological phases in three or more dimensions Iadecola, Thomas; Neupert, Titus; Chamon, Claudio Physical Review B, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevB.93.195136	journal	May 2016
Nondiagonal anisotropic quantum Hall states Tam, Pok Man; Kane, Charles L. Physical Review B, Vol. 103, Issue 3 https://doi.org/10.1103/PhysRevB.103.035142	journal	January 2021
Quantum spin liquids Broholm, C.; Cava, R. J.; Kivelson, S. A. Science, Vol. 367, Issue 6475 https://doi.org/10.1126/science.aay0668	journal	January 2020
Spinons in more than one dimension: Resonance valence bond state stabilized by frustration Nersesyan, A. A.; Tsvelik, A. M. Physical Review B, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevB.67.024422	journal	January 2003
Heisenberg–Kitaev physics in magnetic fields Janssen, Lukas; Vojta, Matthias Journal of Physics: Condensed Matter, Vol. 31, Issue 42 https://doi.org/10.1088/1361-648X/ab283e	journal	July 2019
Two-dimensional spin liquids with $Z_{2}$ topological order in an array of quantum wires Patel, Aavishkar A.; Chowdhury, Debanjan Physical Review B, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevB.94.195130	journal	November 2016
Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions Mross, David F.; Alicea, Jason; Motrunich, Olexei I. Physical Review X, Vol. 7, Issue 4 https://doi.org/10.1103/PhysRevX.7.041016	journal	October 2017
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections Hermanns, M.; Kimchi, I.; Knolle, J. Annual Review of Condensed Matter Physics, Vol. 9, Issue 1 https://doi.org/10.1146/annurev-conmatphys-033117-053934	journal	March 2018
From Luttinger liquid to non-Abelian quantum Hall states Teo, Jeffrey C. Y.; Kane, C. L. Physical Review B, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevB.89.085101	journal	February 2014
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator Chang, C. -Z.; Zhang, J.; Feng, X. Science, Vol. 340, Issue 6129 https://doi.org/10.1126/science.1234414	journal	March 2013
Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms Scholl, Pascal; Schuler, Michael; Williams, Hannah J. Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03585-1	journal	July 2021
Hunting Majorana Fermions in Kitaev Magnets Motome, Yukitoshi; Nasu, Joji Journal of the Physical Society of Japan, Vol. 89, Issue 1 https://doi.org/10.7566/JPSJ.89.012002	journal	January 2020
From an array of quantum wires to three-dimensional fractional topological insulators Sagi, Eran; Oreg, Yuval Physical Review B, Vol. 92, Issue 19 https://doi.org/10.1103/PhysRevB.92.195137	journal	November 2015
Fracton Topological Phases from Strongly Coupled Spin Chains Halász, Gábor B.; Hsieh, Timothy H.; Balents, Leon Physical Review Letters, Vol. 119, Issue 25 https://doi.org/10.1103/PhysRevLett.119.257202	journal	December 2017
Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states Fuji, Yohei; He, Yin-Chen; Bhattacharjee, Subhro Physical Review B, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevB.93.195143	journal	May 2016
A Field Guide to Spin Liquids Knolle, J.; Moessner, R. Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031218-013401	journal	March 2019
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Coupled-wire construction of chiral spin liquids Meng, Tobias; Neupert, Titus; Greiter, Martin Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.241106	journal	June 2015
Microscopic characterization of Ising conformal field theory in Rydberg chains Slagle, Kevin; Aasen, David; Pichler, Hannes Physical Review B, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevB.104.235109	journal	December 2021
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator Fu, Liang; Kane, C. L. Physical Review Letters, Vol. 100, Issue 9 https://doi.org/10.1103/PhysRevLett.100.096407	journal	March 2008
Quantum simulation and computing with Rydberg-interacting qubits Morgado, M.; Whitlock, S. AVS Quantum Science, Vol. 3, Issue 2 https://doi.org/10.1116/5.0036562	journal	May 2021
Chemistry of Quantum Spin Liquids Chamorro, Juan R.; McQueen, Tyrel M.; Tran, Thao T. Chemical Reviews, Vol. 121, Issue 5 https://doi.org/10.1021/acs.chemrev.0c00641	journal	November 2020
Non-Abelian topological insulators from an array of quantum wires Sagi, Eran; Oreg, Yuval Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.201102	journal	November 2014
Coupled-wire description of surface $A D E$ topological order Han, Bo; Teo, Jeffrey C. Y. Physical Review B, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevB.99.235102	journal	June 2019
Fractional Quantum Hall Effect in an Array of Quantum Wires Kane, C. L.; Mukhopadhyay, Ranjan; Lubensky, T. C. Physical Review Letters, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevLett.88.036401	journal	January 2002
Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models Jackeli, G.; Khaliullin, G. Physical Review Letters, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevLett.102.017205	journal	January 2009
Wire deconstructionism of two-dimensional topological phases Neupert, Titus; Chamon, Claudio; Mudry, Christopher Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.205101	journal	November 2014
Gapless chiral spin liquid from coupled chains on the kagome lattice Pereira, Rodrigo; Bieri, Samuel SciPost Physics, Vol. 4, Issue 1 https://doi.org/10.21468/SciPostPhys.4.1.004	journal	January 2018
Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators Mross, David F.; Essin, Andrew; Alicea, Jason Physical Review Letters, Vol. 116, Issue 3 https://doi.org/10.1103/PhysRevLett.116.036803	journal	January 2016
Superconducting Analogue of the Parafermion Fractional Quantum Hall States Vaezi, Abolhassan Physical Review X, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevX.4.031009	journal	July 2014
Integer and fractional quantum Hall effect in a strip of stripes Klinovaja, Jelena; Loss, Daniel The European Physical Journal B, Vol. 87, Issue 8 https://doi.org/10.1140/epjb/e2014-50395-6	journal	August 2014

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