Insensitivity of bulk properties to the twisted boundary condition

TL;DR

This paper proves that in gapped U(1) symmetric quantum systems with finite-range interactions, bulk properties are essentially unaffected by boundary twists in large systems, due to exponential decay of correlations.

Contribution

It establishes the insensitivity of bulk properties to twisted boundary conditions in large gapped U(1) symmetric systems, highlighting the role of correlation decay.

Findings

Bulk properties are independent of the twisted boundary phase in large systems.

Dependence on the twisted angle diminishes exponentially with system size.

Correlation functions decay exponentially, supporting insensitivity.

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.