Annals of Physics最新文献

{"title":"Quantum systems in the hyperbolic phase-space: Explicit maps, differential form of the star product and their applications","authors":"M. Baltazar,&nbsp;I.F. Valtierra,&nbsp;A.B. Klimov","doi":"10.1016/j.aop.2025.170208","DOIUrl":"10.1016/j.aop.2025.170208","url":null,"abstract":"<div><div>We obtain a closed-form expression for the <span><math><mi>s</mi></math></span>-parametrized mapping kernels for the phase-space representation of quantum systems with the SU(1,1) symmetry group, in terms of an expansion over the appropriate tensor operators, which enables us to express the kernels in terms of continuous dual Hahn polynomials. Using this representation, we derive an explicit differential form of the star-product for the SU(1,1) map, which is expandable in the inverse Bargmann index and plays the role of the semiclassical parameter in hyperbolic phase space. This formulation allows us to analyze quantum dynamics through evolved phase-space distributions that obey a Moyal-like equation. We illustrate the star-product by deriving the Bopp operators, which represent the action of the group generators on the kernels, and by discussing the symplectic-like structure of the Moyal equation for Hamiltonians that are linear or quadratic in the SU(1,1) generators. We analyze the semiclassical limit of the Moyal evolution equation and show that, over short-time quantum dynamics, the evolution of the initial distribution along classical trajectories reproduces the quantum behavior; the magnitude of quantum corrections depends on the chosen map and is minimal for the Wigner map. Examples of applications of the developed formalism to the analysis of quantum dynamics governed by non-linear Hamiltonians are discussed.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170208"},"PeriodicalIF":3.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-renormalization of the fractional quantum Hall conductivity by interactions","authors":"M. Selch,&nbsp;M.A. Zubkov,&nbsp;Souvik Pramanik,&nbsp;M. Lewkowicz","doi":"10.1016/j.aop.2025.170202","DOIUrl":"10.1016/j.aop.2025.170202","url":null,"abstract":"<div><div>We investigate the theory of the fractional quantum Hall effect (QHE) proposed a long time ago by Lopez and Fradkin (1991) to describe the principal Jain series. The magnetic fluxes of the statistical gauge field attached to electrons remain at rest in the reference frame moving together with the electron liquid. In the laboratory reference frame the electric field of the statistical gauge field forms and screens the external electric field. The fractional QHE conductivity appears as a consequence of this screening already on the mean field theory level. We consider a relativistic extension of the model, and propose an alternative description of the fractional QHE based on macroscopic motion of the electron liquid within the Zubarev statistical operator approach. It is this macroscopic motion of electrons which in this pattern gives rise to the fractional QHE. Within this approach we propose the proof to all orders of perturbation theory that the interaction corrections cannot change the above mentioned mean field theory result for the QHE conductivity.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170202"},"PeriodicalIF":3.0,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heat engine efficiency and thermodynamical fluctuations of quantum Oppenheimer–Snyder anti-de Sitter spacetime","authors":"Faisal Javed ,&nbsp;Arfa Waseem ,&nbsp;Tayyab Naseer ,&nbsp;M. Zeeshan Gul ,&nbsp;Mansoor H. Alshehri ,&nbsp;Rana Muhammad Zulqarnain","doi":"10.1016/j.aop.2025.170189","DOIUrl":"10.1016/j.aop.2025.170189","url":null,"abstract":"<div><div>This research paper conducts a comprehensive analysis of the thermodynamic features of quantum Oppenheimer–Snyder-AdS black holes, highlighting the effects of Joule–Thomson expansion and higher-order thermal fluctuations. We examine the metric function to investigate the crucial influence of the quantum factor on the determination of the event horizon radius and the overall spacetime geometry. An extensive analysis of the Joule–Thomson coefficients elucidates the intricate gas dynamics near black holes, revealing specific cooling and heating regions. Our findings emphasize the significance of isenthalpic curves in comprehending the energy dynamics related to these occurrences. Furthermore, we examine important thermodynamic functions, like corrected entropy, enthalpy, Helmholtz and Gibbs free energies, internal energy and specific heat capacity. Our examination of corrected entropy demonstrates significant peaks and troughs relative to the radius of the event horizon, substantiating the complex correlation between black hole mass and quantum parameter. The Helmholtz free energy demonstrates considerable oscillations affected by the quantum parameter, but the internal energy indicates enormous energy buildup with an increase in horizon radius. Significant variations in enthalpy and Gibbs free energy are also observed, signifying changes in thermodynamic stability when mass and quantum parameters fluctuate. The specific heat analysis reveals intricate oscillations, indicating critical phase transitions and the thermodynamic stability of the system. These findings underscore the imperative of including quantum effects in black hole thermodynamics, therefore deepening our comprehension of the intricate connection between quantum physics and gravitational events.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170189"},"PeriodicalIF":3.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effective approach to open systems with probability currents and the Grothendieck formalism","authors":"A. Vourdas","doi":"10.1016/j.aop.2025.170207","DOIUrl":"10.1016/j.aop.2025.170207","url":null,"abstract":"<div><div>An effective approach to open systems and irreversible phenomena is presented, where an open system <span><math><mrow><mi>Σ</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mi>d</mi></math></span>-dimensional Hilbert space, is a subsystem of a larger isolated system <span><math><mrow><mi>Σ</mi><mrow><mo>(</mo><mn>2</mn><mi>d</mi><mo>)</mo></mrow></mrow></math></span> (the ‘full universe’) with <span><math><mrow><mn>2</mn><mi>d</mi></mrow></math></span>-dimensional Hilbert space. A family of Bargmann-like representations (called <span><math><mi>z</mi></math></span>-Bargmann representations) introduces naturally the larger space. The <span><math><mi>z</mi></math></span>-Bargmann representations are defined through semi-unitary matrices (which are a coherent states formalism in disguise). The ‘openness’ of the system is quantified with the probability current that flows from the system to the external world. The Grothendieck quantity <span><math><mi>Q</mi></math></span> is shown to be related to the probability current, and is used as a figure of merit for the ‘openness’ of a system. <span><math><mi>Q</mi></math></span> is expressed in terms of ‘rescaling transformations’ which change not only the phase but also the absolute value of the wavefunction, and are intimately linked to irreversible phenomena (e.g., damping/amplification). It is shown that unitary transformations in the isolated system <span><math><mrow><mi>Σ</mi><mrow><mo>(</mo><mn>2</mn><mi>d</mi><mo>)</mo></mrow></mrow></math></span> (full universe), reduce to rescaling transformations when projected to its open subsystem <span><math><mrow><mi>Σ</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span>. The values of the Grothendieck <span><math><mi>Q</mi></math></span> for various quantum states in an open system, are compared with those for their counterpart states in an isolated system.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170207"},"PeriodicalIF":3.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Wormholes in f(T,T) gravity","authors":"F. Parsaei,&nbsp;S. Rastgoo","doi":"10.1016/j.aop.2025.170205","DOIUrl":"10.1016/j.aop.2025.170205","url":null,"abstract":"<div><div>This study aims to investigate the physical properties of wormhole geometry within the context of <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>T</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> gravity, which serves as a teleparallel formulation of general relativity. We study a linear model, <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>T</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>=</mo><mi>α</mi><mi>T</mi><mo>+</mo><mi>β</mi><mi>T</mi></mrow></math></span>, to explore traversable wormholes. A linear equation of state is utilized for radial pressure, leading to a power-law shaped function. It was found that the violation of energy conditions, depends on the <span><math><mi>α</mi></math></span> and <span><math><mi>β</mi></math></span> parameters. A diverse array of intriguing wormhole solutions was identified, contingent upon the specific model parameters employed. It is demonstrated that isotropic wormhole solutions cannot be attained within this framework. Additionally, solutions characterized by a variable equation of state parameter are introduced. A comparative analysis of wormhole solutions in the context of <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>T</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> and curvature-based gravity, specifically <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span>, is also provided.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170205"},"PeriodicalIF":3.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145004827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Schwarzschild-Levi-Civita Metric","authors":"Z. Amirabi","doi":"10.1016/j.aop.2025.170204","DOIUrl":"10.1016/j.aop.2025.170204","url":null,"abstract":"<div><div>This study investigates gravitational lensing and null geodesics in the Schwarzschild-Levi-Civita Metric (SLCM), an axially symmetric solution to the vacuum Einstein equations. The SLCM resembles the Ernst black hole but differs fundamentally in being a vacuum solution rather than one sourced by electromagnetic fields. Utilizing the Gauss–Bonnet theorem and the optical metric approach developed by Gibbons, Werner, and Ishihara et al., the deflection angle of light in the SLCM is derived, including finite-distance corrections for source and observer positions. An explicit analytic expression for the deflection angle is obtained, featuring both Levi-Civita-like terms and corrections from the SLCM’s cosmological horizon. Numerical analysis of null geodesics confirms that all light rays are eventually drawn toward the horizon, regardless of initial velocity direction. These findings offer insights into the lensing properties of axially symmetric, non-asymptotically flat spacetimes in general relativity.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170204"},"PeriodicalIF":3.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shadow of F(R)-Euler–Heisenberg black hole and constraints from EHT observations","authors":"Khadije Jafarzade ,&nbsp;Saira Yasmin ,&nbsp;Mubasher Jamil","doi":"10.1016/j.aop.2025.170198","DOIUrl":"10.1016/j.aop.2025.170198","url":null,"abstract":"<div><div>This study investigates the optical properties of a static, spherically symmetric, electrically charged black hole in <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> gravity, coupled with Euler–Heisenberg (<span><math><mi>EH</mi></math></span>) nonlinear electrodynamics (NLED). By analyzing photon trajectories in this background, we demonstrate how the model parameters influence light propagation, leading to broader ranges for both lensed paths and photon rings. We identify parameter regions that allow for physically consistent black hole shadows, characterized by a photon sphere located outside the event horizon and a shadow forming beyond it. These viable regions expand with increasing electric charge and <span><math><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></math></span>, highlighting the interplay between gravitational and electromagnetic effects. Constraining the model using Event Horizon Telescope (EHT) observations of M87*, we find that de Sitter (dS) black holes remain compatible with the data, whereas anti-de Sitter (AdS) solutions are disfavored under low charge and <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub><mo>&gt;</mo><mo>−</mo><mn>1</mn></mrow></math></span>. Finally, our analysis of the energy emission rate shows that higher electric charge enhances black hole evaporation, while stronger NLED effects and larger <span><math><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></math></span> values suppress it.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170198"},"PeriodicalIF":3.0,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact solution of the Pauli equation in the presence of a magnetic field in a spinning cosmic string spacetime","authors":"M.D. de Oliveira,&nbsp;Alexandre G.M. Schmidt","doi":"10.1016/j.aop.2025.170206","DOIUrl":"10.1016/j.aop.2025.170206","url":null,"abstract":"<div><div>We study the Landau quantization of a spin-1/2 charged particle in the background of a spinning cosmic string, using the Pauli equation. The interaction between the particle’s spin, the magnetic field, and spacetime rotation leads to different radial equations for each component of the Pauli spinor. As a result, the upper and lower spinor components differ, each associated with its own principal quantum number and effective angular momentum. The effective angular momentum is influenced by the magnetic field, cosmic string, space rotation and spin. By analyzing a particular case where the eigenenergies are independent of the spin orientation, we find that the magnetic field must be quantized. These eigenenergies reflect both spin–magnetic field interaction and the influence of spacetime rotation. We examine an asymptotic case between angular momentum and the rotation of space, and we also present a graphical analysis of the magnetic field and the energy levels, comparing cases with and without an internal structure for the cosmic string.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170206"},"PeriodicalIF":3.0,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Role of cosmic voids and their matter properties in shaping wormhole geometry in generalized geometry-matter coupling gravity","authors":"A. Errehymy ,&nbsp;S. Hansraj","doi":"10.1016/j.aop.2025.170200","DOIUrl":"10.1016/j.aop.2025.170200","url":null,"abstract":"<div><div>Cosmic voids are increasingly recognized as a promising tool for cosmological exploration. Their distribution and density profiles are highly responsive to alterations in gravitational theories, along with the influences of dark energy and neutrinos. Investigating voids offers a compelling opportunity to uncover signatures of alternative gravity models on a cosmological level. Voids span a notable range of density contrasts, from approximately <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> near their centers to around 0 at their edges, where screening mechanisms become less effective. The primary objective of this study is to explore a novel model that introduces a new category of wormhole solutions by leveraging cosmic voids – vast underdense regions of the universe – for the first time. We focus on identifying new exact static wormhole models by proposing an alternative viewpoint on their matter content, rooted in the recently formulated <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> theory of gravity. By developing a unique solution based on a universal density profile for voids, we examine crucial constraints on the parameters that dictate matter distribution and the structure of spacetime itself. Our results reveal how these cosmic voids significantly influence the geometry of wormholes, steepening the gradient toward the throat and mitigating violations of the null and weak energy conditions, particularly beyond their centers. We also highlight intriguing gravitational lensing effects, showing that this wormhole repels light rather than capturing it, creating a fascinating interaction between gravity and light. Furthermore, we investigate the stability of the solution using the TOV formalism, along with the effects of exotic matter, the exoticity parameter, and anisotropy on wormhole geometry. These insights contribute to a deeper understanding of wormhole behavior in underdense environments and the pivotal role cosmic voids play in their formation.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170200"},"PeriodicalIF":3.0,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144926259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optically controlled topological phases in the deformed α-T3 lattice","authors":"O. Benhaida ,&nbsp;E.H. Saidi ,&nbsp;L.B. Drissi","doi":"10.1016/j.aop.2025.170203","DOIUrl":"10.1016/j.aop.2025.170203","url":null,"abstract":"<div><div>Haldane’s tight-binding model, which describes a Chern insulator in a two-dimensional hexagonal lattice, exhibits quantum Hall conductivity without an external magnetic field. Here, we explore an <span><math><mrow><mi>α</mi><mo>−</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> lattice subjected to circularly polarized off-resonance light. This lattice, composed of two sublattices (A and B) and a central site (C) per unit cell, undergoes deformation by varying the hopping parameter <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> while keeping <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mi>γ</mi></mrow></math></span>. Analytical expressions for quasi-energies in the first Brillouin zone reveal significant effects of symmetry breaking. Circularly polarized light lifts the degeneracy of Dirac points, shifting the cones from M. This deformation evolves with <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, breaking symmetry at <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>2</mn><mi>γ</mi></mrow></math></span>, as observed in Berry curvature diagrams. In the standard case (<span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mi>γ</mi></mrow></math></span>), particle-hole and inversion symmetries are preserved for <span><math><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></math></span>. The system transitions from a semi-metal to a Chern insulator, with band-specific Chern numbers: <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span> for <span><math><mrow><mi>α</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>,</mo></mrow></math></span> shifting to <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>2</mn></mrow></math></span> when <span><math><mrow><mi>α</mi><mo>⩾</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>.</mo></mrow></math></span>For <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&gt;</mo><mn>2</mn><mi>γ</mi></mrow></math></span>, the system enters a trivial insulating phase. These tr","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"482 ","pages":"Article 170203"},"PeriodicalIF":3.0,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145004828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}