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Petiziol F. Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids. PHYSICAL REVIEW LETTERS 2024; 133:036601. [PMID: 39094173 DOI: 10.1103/physrevlett.133.036601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2024] [Revised: 04/26/2024] [Accepted: 05/30/2024] [Indexed: 08/04/2024]
Abstract
We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as π fluxes; namely, they result in the accumulation of a π phase if wound around each other. Non-Abelian behavior emerges because the Floquet modulation can engineer a nontrivial band topology for the fermions, inducing their fractionalization into Floquet-Majorana modes bound to the bosons. The latter then develop non-Abelian character akin to vortices in topological superconductors, realizing Ising topological order. Our findings shed light on the nonequilibrium physics of driven topologically ordered quantum matter and may facilitate the observation of non-Abelian behavior in engineered quantum systems.
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Adelhardt P, Koziol JA, Langheld A, Schmidt KP. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. ENTROPY (BASEL, SWITZERLAND) 2024; 26:401. [PMID: 38785650 PMCID: PMC11120707 DOI: 10.3390/e26050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 04/17/2024] [Accepted: 04/19/2024] [Indexed: 05/25/2024]
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.
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Affiliation(s)
| | | | | | - Kai P. Schmidt
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; (P.A.); (J.A.K.); (A.L.)
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Cong I, Maskara N, Tran MC, Pichler H, Semeghini G, Yelin SF, Choi S, Lukin MD. Enhancing detection of topological order by local error correction. Nat Commun 2024; 15:1527. [PMID: 38378727 PMCID: PMC10879205 DOI: 10.1038/s41467-024-45584-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Accepted: 01/25/2024] [Indexed: 02/22/2024] Open
Abstract
The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a paradigm for quantifying topological states-locally error-corrected decoration (LED)-by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.
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Affiliation(s)
- Iris Cong
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Minh C Tran
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Hannes Pichler
- Institute for Theoretical Physics, University of Innsbruck, 6020, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020, Innsbruck, Austria
| | - Giulia Semeghini
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Susanne F Yelin
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Soonwon Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA.
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Steinert LM, Osterholz P, Eberhard R, Festa L, Lorenz N, Chen Z, Trautmann A, Gross C. Spatially Tunable Spin Interactions in Neutral Atom Arrays. PHYSICAL REVIEW LETTERS 2023; 130:243001. [PMID: 37390432 DOI: 10.1103/physrevlett.130.243001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 01/20/2023] [Accepted: 05/16/2023] [Indexed: 07/02/2023]
Abstract
Analog quantum simulations with Rydberg atoms in optical tweezers routinely address strongly correlated many-body problems due to the hardware-efficient implementation of the Hamiltonian. Yet, their generality is limited, and flexible Hamiltonian-design techniques are needed to widen the scope of these simulators. Here we report on the realization of spatially tunable interactions for XYZ models implemented by two-color near-resonant coupling to Rydberg pair states. Our results demonstrate the unique opportunities of Rydberg dressing for Hamiltonian design in analog quantum simulators.
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Affiliation(s)
- Lea-Marina Steinert
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Philip Osterholz
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Robin Eberhard
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Lorenzo Festa
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Nikolaus Lorenz
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Zaijun Chen
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Arno Trautmann
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
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Yu XJ, Ding C, Xu L. Quantum criticality of a Z_{3}-symmetric spin chain with long-range interactions. Phys Rev E 2023; 107:054122. [PMID: 37329095 DOI: 10.1103/physreve.107.054122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/28/2023] [Indexed: 06/18/2023]
Abstract
Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power α increases, the critical points f_{c}^{*} shift towards lower values. In addition, the critical threshold α_{c}(≈1.43) of the long-range interaction power is obtained for the first time by a nonperturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range (α<α_{c}) and short-range (α>α_{c}) universality classes, qualitatively consistent with the classical ϕ^{3} effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.
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Affiliation(s)
- Xue-Jia Yu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Chengxiang Ding
- School of Science and Engineering of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243002, China
| | - Limei Xu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing, China
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing, China
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