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Yao H, Tanzi L, Sanchez-Palencia L, Giamarchi T, Modugno G, D'Errico C. Mott Transition for a Lieb-Liniger Gas in a Shallow Quasiperiodic Potential: Delocalization Induced by Disorder. PHYSICAL REVIEW LETTERS 2024; 133:123401. [PMID: 39373444 DOI: 10.1103/physrevlett.133.123401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 07/09/2024] [Indexed: 10/08/2024]
Abstract
Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum Monte Carlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.
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Affiliation(s)
| | | | | | | | - Giovanni Modugno
- Istituto Nazionale di Ottica, CNR-INO, Via Moruzzi 1, 56124 Pisa, Italy
- European Laboratory for Non-Linear Spectroscopy, Università degli Studi di Firenze, Via N. Carrara 1, 50019 Sesto Fiorentino, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy
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2
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Roy K, Roy S, Basu S. Quasiperiodic disorder induced critical phases in a periodically driven dimerized p-wave Kitaev chain. Sci Rep 2024; 14:20603. [PMID: 39232007 PMCID: PMC11375019 DOI: 10.1038/s41598-024-70995-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 08/22/2024] [Indexed: 09/06/2024] Open
Abstract
The intricate relationship between topology and disorder in non-equilibrium quantum systems presents a captivating avenue for exploring localization phenomenon. Here, we look for a suitable platform that enables an in-depth investigation of the topic. To this end, we delve into the nuanced analysis of the topological and localization characteristics exhibited by a one-dimensional dimerized Kitaev chain under periodic driving and perform detailed analyses of the Floquet Majorana modes. Such a non-equilibrium scenario is made further interesting by including a spatially varying quasiperiodic potential with a temporally modulated amplitude. Apriori, the motivation is to explore an interplay between dimerization and a quasiperiodic disorder in a topological setting which is also known to demonstrate unique (re-entrant) localization properties. While the topological properties of the driven system confirm the presence of zero and π Majorana modes, the phase diagram obtained by constructing a pair of topological invariants ( Z × Z ), also referred to as the real space winding numbers, at different driving frequencies reveal intriguing features that are distinct from the static scenario. In particular, at either low or intermediate frequency regimes, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the Majorana π mode unveils the emergence of a unique topological phase, characterized by complete localization of both the bulk and the edge modes, which may be called as the Floquet topological Anderson phase. Moreover, different frequency regimes showcase distinct localization features which can be examined via the localization toolbox, namely, the inverse and the normalized participation ratios. Specifically, the low and high-frequency regimes demonstrate the existence of completely extended and localized phases, respectively. While at intermediate frequencies, we observe the critical (multifractal) phase of the model which is further investigated via a finite-size scaling analysis of the fractal dimension. Finally, to add depth into our study, we have performed a mean level spacing analyses and computed the Hausdorff dimension which yields specific characteristics inherent to the critical phase, offering profound insights into its underlying properties.
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Affiliation(s)
- Koustav Roy
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India.
| | - Shilpi Roy
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India
- Department of Physics, National University of Singapore, 117542, Singapore, Singapore
| | - Saurabh Basu
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India
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3
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Zhang YC. Critical regions in a one-dimensional flat band lattice with a quasi-periodic potential. Sci Rep 2024; 14:17921. [PMID: 39095462 PMCID: PMC11297334 DOI: 10.1038/s41598-024-68851-4] [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: 04/23/2024] [Accepted: 07/29/2024] [Indexed: 08/04/2024] Open
Abstract
In our previous work, the concept of critical region in a generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) has been established. In this work, we find that the critical region can be realized in a one-dimensional flat band lattice with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced to an effective Ganeshan-Pixley-Das Sarma's model. Depending on various parameter ranges, the effective quasi-periodic potential may be bounded or unbounded. In these two cases, the Lyapunov exponent, mobility edge, and critical indices of localized length are obtained exactly. In this flat band model, the localized-extended, localized-critical and critical-extended transitions can coexist. Furthermore, we find that near the transitions between the bound and unbounded cases, the derivative of Lyapunov exponent of localized states with respect to energy is discontinuous. At the end, the localized states in bounded and unbounded cases can be distinguished from each other by Avila's acceleration.
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Affiliation(s)
- Yi-Cai Zhang
- School of Physics and Materials Science, Guangzhou University, Guangzhou, 510006, People's Republic of China.
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4
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Longhi S. Dephasing-Induced Mobility Edges in Quasicrystals. PHYSICAL REVIEW LETTERS 2024; 132:236301. [PMID: 38905645 DOI: 10.1103/physrevlett.132.236301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 05/10/2024] [Indexed: 06/23/2024]
Abstract
Mobility edges (ME), separating Anderson-localized states from extended states, are known to arise in the single-particle energy spectrum of certain one-dimensional lattices with aperiodic order. Dephasing and decoherence effects are widely acknowledged to spoil Anderson localization and to enhance transport, suggesting that ME and localization are unlikely to be observable in the presence of dephasing. Here it is shown that, contrary to such a wisdom, ME can be created by pure dephasing effects in quasicrystals in which all states are delocalized under coherent dynamics. Since the lifetimes of localized states induced by dephasing effects can be extremely long, rather counterintuitively decoherence can enhance localization of excitation in the lattice. The results are illustrated by considering photonic quantum walks in synthetic mesh lattices.
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Liu Y, Wang Z, Yang C, Jie J, Wang Y. Dissipation-Induced Extended-Localized Transition. PHYSICAL REVIEW LETTERS 2024; 132:216301. [PMID: 38856294 DOI: 10.1103/physrevlett.132.216301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Revised: 02/05/2024] [Accepted: 04/23/2024] [Indexed: 06/11/2024]
Abstract
A mobility edge (ME), representing the critical energy that distinguishes between extended and localized states, is a key concept in understanding the transition between extended (metallic) and localized (insulating) states in disordered and quasiperiodic systems. Here we explore the impact of dissipation on a quasiperiodic system featuring MEs by calculating steady-state density matrix and analyzing quench dynamics with sudden introduction of dissipation. We demonstrate that dissipation can lead the system into specific states predominantly characterized by either extended or localized states, irrespective of the initial state. Our results establish the use of dissipation as a new avenue for inducing transitions between extended and localized states and for manipulating dynamic behaviors of particles.
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Affiliation(s)
- Yaru Liu
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Intense Laser Application Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - Zeqing Wang
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - Chao Yang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jianwen Jie
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Intense Laser Application Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - Yucheng Wang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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6
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Gonçalves M, Amorim B, Castro EV, Ribeiro P. Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models. PHYSICAL REVIEW LETTERS 2023; 131:186303. [PMID: 37977623 DOI: 10.1103/physrevlett.131.186303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 09/25/2023] [Indexed: 11/19/2023]
Abstract
We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of Sriram Ganeshan, J. H. Pixley, and S. Das Sarma [Phys. Rev. Lett. 114, 146601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.146601] and J. Biddle and S. Das Sarma [Phys. Rev. Lett. 104, 070601 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.070601]. The analytical treatment follows from recognizing these models as a novel type of fixed points of the renormalization group procedure recently proposed in Phys. Rev. B 108, L100201 (2023)10.1103/PhysRevB.108.L100201 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and nontrivial mobility edges in an undriven system without the need for the unbounded potentials required by previous proposals.
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Affiliation(s)
- Miguel Gonçalves
- CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- Centro de Física das Universidades do Minho e Porto, LaPMET, Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
| | - Bruno Amorim
- Centro de Física das Universidades do Minho e Porto, LaPMET, University of Minho, Campus of Gualtar, 4710-057 Braga, Portugal
| | - Eduardo V Castro
- Centro de Física das Universidades do Minho e Porto, LaPMET, Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Pedro Ribeiro
- CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- Beijing Computational Science Research Center, Beijing 100193, China
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7
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Zhou XC, Wang Y, Poon TFJ, Zhou Q, Liu XJ. Exact New Mobility Edges between Critical and Localized States. PHYSICAL REVIEW LETTERS 2023; 131:176401. [PMID: 37955469 DOI: 10.1103/physrevlett.131.176401] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 08/25/2023] [Accepted: 09/29/2023] [Indexed: 11/14/2023]
Abstract
The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by a quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This Letter may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.
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Affiliation(s)
- Xin-Chi Zhou
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
| | - Yongjian Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China
| | - Ting-Fung Jeffrey Poon
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
| | - Qi Zhou
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
- International Quantum Academy, Shenzhen 518048, China
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8
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Zhu Z, Yao H, Sanchez-Palencia L. Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential. PHYSICAL REVIEW LETTERS 2023; 130:220402. [PMID: 37327407 DOI: 10.1103/physrevlett.130.220402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 05/10/2023] [Indexed: 06/18/2023]
Abstract
Quantum simulation of quasicrystals in synthetic bosonic matter now paves the way for the exploration of these intriguing systems in wide parameter ranges. Yet thermal fluctuations in such systems compete with quantum coherence and significantly affect the zero-temperature quantum phases. Here we determine the thermodynamic phase diagram of interacting bosons in a two-dimensional, homogeneous quasicrystal potential. We find our results using quantum Monte Carlo simulations. Finite-size effects are carefully taken into account and the quantum phases are systematically distinguished from thermal phases. In particular, we demonstrate stabilization of a genuine Bose glass phase against the normal fluid in sizable parameter ranges. We interpret our results for strong interactions using a fermionization picture and discuss experimental relevance.
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Affiliation(s)
- Zhaoxuan Zhu
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
| | - Hepeng Yao
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
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9
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Cai X, Yu YC. Exact mobility edges in quasiperiodic systems without self-duality. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:035602. [PMID: 36347043 DOI: 10.1088/1361-648x/aca136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 11/08/2022] [Indexed: 06/16/2023]
Abstract
Mobility edge (ME), a critical energy separating localized and extended states in spectrum, is a central concept in understanding localization physics. However, there are few models with exact MEs, and their presences are fragile against perturbations. In the paper, we generalize the Aubry-André-Harper model proposed in (Ganeshanet al2015Phys. Rev. Lett.114146601) and recently realized in (Anet al2021Phys. Rev. Lett.126040603), by introducing a relative phase in the quasiperiodic potential. Applying Avila's global theory, we analytically compute localization lengths of all single-particle states and determine the exact expression of ME, which both significantly depend on the relative phase. They are verified by numerical simulations, and physical perception of the exact expression is also provided. We show that old exact MEs, guaranteed by the delicate self-duality which is broken by the relative phase, are special ones in a series controlled by the phase. Furthermore, we demonstrate that out of expectation, exact MEs are invariant against a shift in the quasiperiodic potential, although the shift changes the spectrum and localization properties. Finally, we show that the exact ME is related to the one in the dual model which has long-range hoppings.
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Affiliation(s)
- Xiaoming Cai
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
| | - Yi-Cong Yu
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
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10
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Wang Y, Zhang JH, Li Y, Wu J, Liu W, Mei F, Hu Y, Xiao L, Ma J, Chin C, Jia S. Observation of Interaction-Induced Mobility Edge in an Atomic Aubry-André Wire. PHYSICAL REVIEW LETTERS 2022; 129:103401. [PMID: 36112456 DOI: 10.1103/physrevlett.129.103401] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
A mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. The Aubry-André (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for a mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of a mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our Letter also offers new possibilities to engineer quantum transport and phase transitions in disordered systems.
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Affiliation(s)
- Yunfei Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
| | - Jia-Hui Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
| | - Yuqing Li
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jizhou Wu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Wenliang Liu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Ying Hu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jie Ma
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Cheng Chin
- James Franck Institute, Enrico Fermi Institute, Department of Physics, University of Chicago, Illinois 60637, USA
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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11
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Tang Q, He Y. Mobility edges in one-dimensional models with quasi-periodic disorder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:185505. [PMID: 33711823 DOI: 10.1088/1361-648x/abee3c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 03/12/2021] [Indexed: 06/12/2023]
Abstract
We study the mobility edges in a variety of one-dimensional tight binding models with slowly varying quasi-periodic disorders. It is found that the quasi-periodic disordered models can be approximated by an ensemble of periodic models. The mobility edges can be determined by the overlaps of the energy bands of these periodic models. We demonstrate that this method provides an efficient way to find out the precise location of mobility edge in quasi-periodic disordered models. Based on this approximate method, we also propose an index to indicate the degree of localization of each eigenstate.
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Affiliation(s)
- Qiyun Tang
- College of Physics, Sichuan University, Chengdu, Sichuan 610064, People's Republic of China
| | - Yan He
- College of Physics, Sichuan University, Chengdu, Sichuan 610064, People's Republic of China
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12
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Gautier R, Yao H, Sanchez-Palencia L. Strongly Interacting Bosons in a Two-Dimensional Quasicrystal Lattice. PHYSICAL REVIEW LETTERS 2021; 126:110401. [PMID: 33798372 DOI: 10.1103/physrevlett.126.110401] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
Quasicrystals exhibit exotic properties inherited from the self-similarity of their long-range ordered, yet aperiodic, structure. The recent realization of optical quasicrystal lattices paves the way to the study of correlated Bose fluids in such structures, but the regime of strong interactions remains largely unexplored, both theoretically and experimentally. Here, we determine the quantum phase diagram of two-dimensional correlated bosons in an eightfold quasicrystal potential. Using large-scale quantum Monte Carlo calculations, we demonstrate a superfluid-to-Bose glass transition and determine the critical line. Moreover, we show that strong interactions stabilize Mott insulator phases, some of which have spontaneously broken eightfold symmetry. Our results are directly relevant to current generation experiments and, in particular, drive prospects to the observation of the still elusive Bose glass phase in two dimensions and exotic Mott phases.
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Affiliation(s)
- Ronan Gautier
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
| | - Hepeng Yao
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
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13
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An FA, Padavić K, Meier EJ, Hegde S, Ganeshan S, Pixley JH, Vishveshwara S, Gadway B. Interactions and Mobility Edges: Observing the Generalized Aubry-André Model. PHYSICAL REVIEW LETTERS 2021; 126:040603. [PMID: 33576679 DOI: 10.1103/physrevlett.126.040603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 12/04/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-André model, with an energy-dependent self-duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing low and high energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of high energy states due to screening. This study paves the way for quantitative studies of interaction effects on self-duality induced mobility edges.
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Affiliation(s)
- Fangzhao Alex An
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Karmela Padavić
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Eric J Meier
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Suraj Hegde
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Sriram Ganeshan
- Physics Department, City College of the CUNY, New York, New York 10031, USA
- CUNY Graduate Center, New York, New York 10031, USA
| | - J H Pixley
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Smitha Vishveshwara
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Bryce Gadway
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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14
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Wang Y, Xia X, Zhang L, Yao H, Chen S, You J, Zhou Q, Liu XJ. One-Dimensional Quasiperiodic Mosaic Lattice with Exact Mobility Edges. PHYSICAL REVIEW LETTERS 2020; 125:196604. [PMID: 33216579 DOI: 10.1103/physrevlett.125.196604] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Revised: 08/30/2020] [Accepted: 10/15/2020] [Indexed: 06/11/2023]
Abstract
The mobility edges (MEs) in energy that separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results that allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avila's global theory and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.
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Affiliation(s)
- Yucheng Wang
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xu Xia
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Long Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hepeng Yao
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay 91128 Palaiseau, France
| | - Shu Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China
| | - Jiangong You
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Qi Zhou
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Xiong-Jun Liu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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15
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Yao H, Giamarchi T, Sanchez-Palencia L. Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes. PHYSICAL REVIEW LETTERS 2020; 125:060401. [PMID: 32845659 DOI: 10.1103/physrevlett.125.060401] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Accepted: 07/13/2020] [Indexed: 06/11/2023]
Abstract
The emergence of a compressible insulator phase, known as the Bose glass, is characteristic of the interplay of interactions and disorder in correlated Bose fluids. While widely studied in tight-binding models, its observation remains elusive owing to stringent temperature effects. Here we show that this issue may be overcome by using Lieb-Liniger bosons in shallow quasiperiodic potentials. A Bose glass, surrounded by superfluid and Mott phases, is found above a critical potential and for finite interactions. At finite temperature, we show that the melting of the Mott lobes is characteristic of a fractal structure and find that the Bose glass is robust against thermal fluctuations up to temperatures accessible in quantum gases. Our results raise questions about the universality of the Bose glass transition in such shallow quasiperiodic potentials.
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Affiliation(s)
- Hepeng Yao
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay 91128 Palaiseau, France
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
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16
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Agrawal U, Gopalakrishnan S, Vasseur R. Universality and quantum criticality in quasiperiodic spin chains. Nat Commun 2020; 11:2225. [PMID: 32376859 PMCID: PMC7203221 DOI: 10.1038/s41467-020-15760-5] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Accepted: 03/27/2020] [Indexed: 11/13/2022] Open
Abstract
Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.
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Affiliation(s)
- Utkarsh Agrawal
- Department of Physics, University of Massachusetts, Amherst, Massachusetts, 01003, USA.
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York, 10314, USA
- Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York, 10016, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts, 01003, USA
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