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Wang CY, Zhou TG, Zhou YN, Zhang P. Distinguishing Quantum Phases through Cusps in Full Counting Statistics. PHYSICAL REVIEW LETTERS 2024; 133:083402. [PMID: 39241720 DOI: 10.1103/physrevlett.133.083402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 07/26/2024] [Indexed: 09/09/2024]
Abstract
Measuring physical observables requires averaging experimental outcomes over numerous identical measurements. The complete distribution function of possible outcomes or its Fourier transform, known as the full counting statistics, provides a more detailed description. This method captures the fundamental quantum fluctuations in many-body systems and has gained significant attention in quantum transport research. In this Letter, we propose that cusp singularities in the full counting statistics are a novel tool for distinguishing between ordered and disordered phases. As a specific example, we focus on the superfluid-to-Mott transition in the Bose-Hubbard model. Through both analytical analysis and numerical simulations, we demonstrate that the full counting statistics exhibit a cusp singularity as a function of the phase angle in the superfluid phase when the subsystem size is sufficiently large, while it remains smooth in the Mott phase. This discontinuity can be interpreted as a first-order transition between different semiclassical configurations of vortices. We anticipate that our discoveries can be readily tested using state-of-the-art ultracold atom and superconducting qubit platforms.
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Affiliation(s)
| | | | | | - Pengfei Zhang
- Department of Physics, Fudan University, Shanghai 200438, China
- Center for Field Theory and Particle Physics, Fudan University, Shanghai 200438, China
- Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
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Liu ZH, Da Liao Y, Pan G, Song M, Zhao J, Jiang W, Jian CM, You YZ, Assaad FF, Meng ZY, Xu C. Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation. PHYSICAL REVIEW LETTERS 2024; 132:156503. [PMID: 38683001 DOI: 10.1103/physrevlett.132.156503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 11/22/2023] [Accepted: 03/23/2024] [Indexed: 05/01/2024]
Abstract
The "symmetric mass generation" (SMG) quantum phase transition discovered in recent years has attracted great interest from both condensed matter and high energy theory communities. Here, interacting Dirac fermions acquire a gap without condensing any fermion bilinear mass term or any concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address in this Letter is whether the SMG transition corresponds to a true unitary conformal field theory. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true (2+1)d unitary conformal field theory.
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Affiliation(s)
- Zi Hong Liu
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Yuan Da Liao
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Gaopei Pan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Menghan Song
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Jiarui Zhao
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Weilun Jiang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
| | - Chao-Ming Jian
- Department of Physics, Cornell University, Ithaca, New York, USA
| | - Yi-Zhuang You
- Department of Physics, University of California, San Diego, California 92093, USA
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Cenke Xu
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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Fan R, Sahay R, Vishwanath A. Extracting the Quantum Hall Conductance from a Single Bulk Wave Function. PHYSICAL REVIEW LETTERS 2023; 131:186301. [PMID: 37977617 DOI: 10.1103/physrevlett.131.186301] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Revised: 08/30/2023] [Accepted: 09/06/2023] [Indexed: 11/19/2023]
Abstract
We propose a new formula that extracts the quantum Hall conductance from a single (2+1)D gapped wave function. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow, i.e., unitary dynamics generated from the entanglement structure of the wave function. The formula is shown to satisfy all formal properties of the Hall conductance: it is odd under time reversal and reflection, even under charge conjugation, universal and topologically rigid in the thermodynamic limit. Further evidence for relating the formula to the Hall conductance is obtained from conformal field theory arguments. Finally, we numerically check the formula by applying it to a noninteracting Chern band where excellent agreement is obtained.
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Affiliation(s)
- Ruihua Fan
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Rahul Sahay
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ashvin Vishwanath
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Liu ZH, Jiang W, Chen BB, Rong J, Cheng M, Sun K, Meng ZY, Assaad FF. Fermion Disorder Operator at Gross-Neveu and Deconfined Quantum Criticalities. PHYSICAL REVIEW LETTERS 2023; 130:266501. [PMID: 37450825 DOI: 10.1103/physrevlett.130.266501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Revised: 04/19/2023] [Accepted: 06/08/2023] [Indexed: 07/18/2023]
Abstract
The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points (QCPs) [W. Jiang et al., arXiv:2209.07103]. Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of the disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole-free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.
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Affiliation(s)
- Zi Hong Liu
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Weilun Jiang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Bin-Bin Chen
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Junchen Rong
- Institut des Hautes Études Scientifiques, 91440 Bures-sur-Yvette, France
| | - Meng Cheng
- Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA
| | - Kai Sun
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
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Yan Z, Meng ZY. Unlocking the general relationship between energy and entanglement spectra via the wormhole effect. Nat Commun 2023; 14:2360. [PMID: 37095103 PMCID: PMC10126136 DOI: 10.1038/s41467-023-37756-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2022] [Accepted: 03/27/2023] [Indexed: 04/26/2023] Open
Abstract
Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane's conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.
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Affiliation(s)
- Zheng Yan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China.
- Department of Physics, School of Science, Westlake University, 600 Dunyu Road, Hangzhou, 310030, Zhejiang Province, China.
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang Province, China.
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China.
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