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Liu Z, Huang RZ, Wang YC, Yan Z, Yao DX. Measuring the Boundary Gapless State and Criticality via Disorder Operator. PHYSICAL REVIEW LETTERS 2024; 132:206502. [PMID: 38829100 DOI: 10.1103/physrevlett.132.206502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Revised: 02/22/2024] [Accepted: 04/22/2024] [Indexed: 06/05/2024]
Abstract
The disorder operator is often designed to reveal the conformal field theory (CFT) information in quantum many-body systems. By using large-scale quantum Monte Carlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but it keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)_{1} CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.
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Affiliation(s)
- Zenan Liu
- Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University, Guangzhou, 510275, China
| | - Rui-Zhen Huang
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium
| | - Yan-Cheng Wang
- Hangzhou International Innovation Institute, Beihang University, Hangzhou 311115, China
- Tianmushan Laboratory, Hangzhou 311115, China
| | - Zheng Yan
- Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou 310030, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, China
| | - Dao-Xin Yao
- Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University, Guangzhou, 510275, China
- International Quantum Academy, Shenzhen 518048, 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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D'Emidio J, Orús R, Laflorencie N, de Juan F. Universal Features of Entanglement Entropy in the Honeycomb Hubbard Model. PHYSICAL REVIEW LETTERS 2024; 132:076502. [PMID: 38427869 DOI: 10.1103/physrevlett.132.076502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Revised: 12/18/2023] [Accepted: 01/26/2024] [Indexed: 03/03/2024]
Abstract
The entanglement entropy is a unique probe to reveal universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many such universal features have yet to be observed. In this Letter we tackle this challenge by introducing a new method to compute the Rényi entanglement entropy in auxiliary-field quantum Monte Carlo simulations, where we treat the entangling region itself as a stochastic variable. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two-dimensional model of interacting fermions, focusing on the half-filled honeycomb Hubbard model at T=0. We detect the universal corner contribution due to gapless fermions throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, where the latter shows a pronounced enhancement depending on the type of entangling cut. Finally, we observe the universal Goldstone mode contribution in the antiferromagnetic Mott insulating phase.
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Affiliation(s)
- Jonathan D'Emidio
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
| | - Román Orús
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
- Multiverse Computing, Paseo de Miramón 170, E-20014 Donostia-San Sebastián, Spain
| | - Nicolas Laflorencie
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
| | - Fernando de Juan
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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Bueno P, Casini H, Andino OL, Moreno J. Conformal Bounds in Three Dimensions from Entanglement Entropy. PHYSICAL REVIEW LETTERS 2023; 131:171601. [PMID: 37955507 DOI: 10.1103/physrevlett.131.171601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Revised: 09/08/2023] [Accepted: 09/29/2023] [Indexed: 11/14/2023]
Abstract
The entanglement entropy of an arbitrary spacetime region A in a three-dimensional conformal field theory (CFT) contains a constant universal coefficient, F(A). For general theories, the value of F(A) is minimized when A is a round disk, F_{0}, and in that case it coincides with the Euclidean free energy on the sphere. We conjecture that, for general CFTs, the quantity F(A)/F_{0} is bounded above by the free scalar field result and below by the Maxwell field one. We provide strong evidence in favor of this claim and argue that an analogous conjecture in the four-dimensional case is equivalent to the Hofman-Maldacena bounds. In three dimensions, our conjecture gives rise to similar bounds on the quotients of various constants characterizing the CFT. In particular, it implies that the quotient of the stress-tensor two-point function coefficient and the sphere free energy satisfies C_{T}/F_{0}≤3/(4π^{2}log2-6ζ[3])≃0.14887 for general CFTs. We verify the validity of this bound for free scalars and fermions, general O(N) and Gross-Neveu models, holographic theories, N=2 Wess-Zumino models and general ABJM theories.
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Affiliation(s)
- Pablo Bueno
- Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
| | - Horacio Casini
- Instituto Balseiro, Centro Atómico Bariloche, 8400-S.C. de Bariloche, Río Negro, Argentina
| | - Oscar Lasso Andino
- Escuela de Ciencias Físicas y Matemáticas,Universidad de Las Américas, Redondel del ciclista, Antigua vía a Nayón, C.P. 170504, Quito, Ecuador
| | - Javier Moreno
- Department of Physics and Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 31905, Israel
- Department of Physics, Technion, Israel Institute of Technology, Haifa 32000, Israel
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Abreu LD. Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles. LETTERS IN MATHEMATICAL PHYSICS 2023; 113:54. [PMID: 37187995 PMCID: PMC10182133 DOI: 10.1007/s11005-023-01674-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Revised: 03/16/2023] [Accepted: 04/11/2023] [Indexed: 05/17/2023]
Abstract
We show that, for a class of planar determinantal point processes (DPP) X , the growth of the entanglement entropy S ( X ( Ω ) ) of X on a compact region Ω ⊂ R 2 d , is related to the variance V X ( Ω ) as follows: V X ( Ω ) ≲ S X ( Ω ) ≲ V X ( Ω ) . Therefore, such DPPs satisfy an area law S X g ( Ω ) ≲ ∂ Ω , where ∂ Ω is the boundary of Ω if they are of Class I hyperuniformity (V X ( Ω ) ≲ ∂ Ω ), while the area law is violated if they are of Class II hyperuniformity (as L → ∞ , V X ( L Ω ) ∼ C Ω L d - 1 log L ). As a result, the entanglement entropy of Weyl-Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity.
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Affiliation(s)
- Luís Daniel Abreu
- NuHAG, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
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Chen BB, Tu HH, Meng ZY, Cheng M. Topological disorder parameter: A many-body invariant to characterize gapped quantum phases. PHYSICAL REVIEW B 2022; 106:094415. [DOI: 10.1103/physrevb.106.094415] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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