Insensitivity of bulk properties to the twisted boundary condition

Abstract

The symmetry and the locality are the two major sources of various nontrivial statements in quantum many-body systems. We demonstrate that, in gapped phases of a U(1) symmetric Hamiltonian with finite-range interactions, the bulk properties such as the expectation value of local operators, the ground state energy and the excitation gap, and the static and low-frequency dynamical responses in general, do not depend on the U(1) phase of the twisted boundary condition in the limit of the large system size. Specifically, their dependence on the twisted angle is exponentially suppressed with the linear dimension of the system. The argument is based on the exponential decay of various types of equal-time correlation functions.

8+6 pages, 1 figure; v3: several typos in Appendices are corrected

References in corpus (12)

• Topological Insulators with Inversion Symmetry
• Fractional quantum Hall states at zero magnetic field
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Correlation effects in two-dimensional topological insulators
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Insulator, conductor and commensurability: a topological approach

Cited by in corpus (40)

• Relations between topology and the quantum metric for Chern insulators
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Non-Hermitian fractional quantum Hall states
• Detecting fractional Chern insulators through circular dichroism
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• Many-body Chern number without integration
• Higher-dimensional generalizations of the Berry curvature
• Bounds in Nonequilibrium Quantum Dynamics
• Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
• Localization, topology and quantized transport in disordered Floquet systems
• Probing localization and quantum geometry by spectroscopy
• A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Geometric orbital magnetization in adiabatic processes
• Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems
• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• (SPT-)LSM theorems from projective non-invertible symmetries
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Duality viewpoint of criticality
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry
• Bosonization with a background $U(1)$ gauge field
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Many-body multipole index and bulk-boundary correspondence
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• Generalized Kramers-Wannier Duality from Bilinear Phase Map
• Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries
• Thouless pumping in Josephson junction arrays
• Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• Higher-dimensional generalizations of the Thouless charge pump
• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities
• Spatial Decay of Kubo's Canonical Correlation Function
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• Superconducting Berry Curvature Dipole
• Crossover from Integer to Fractional Quantum Hall Effect