Off-Diagonal Long-Range Order Implies Vanishing Charge Gap
Quantum Gases
2021-11-17 v3 Statistical Mechanics
Strongly Correlated Electrons
Superconductivity
Quantum Physics
Abstract
For a large class of quantum many-body systems with U(1) symmetry, we prove a general inequality that relates the (off-diagonal) long-range order with the charge gap. For a system of bosons or fermions on a lattice or in the continuum, the inequality implies that a ground state with off-diagonal long-range order inevitably has a vanishing charge gap, and hence is characterized by nonzero charge susceptibility. For a quantum spin system, the inequality implies that a ground state within a magnetization plateau cannot have transverse long-range order.
Cite
@article{arxiv.2105.10692,
title = {Off-Diagonal Long-Range Order Implies Vanishing Charge Gap},
author = {Hal Tasaki and Haruki Watanabe},
journal= {arXiv preprint arXiv:2105.10692},
year = {2021}
}
Comments
10 pages, no figures. Minor imporvments in versions 2 and 3. There is a 16 minutes video in which the main results of the paper are described. See https://youtu.be/fvZdgV8Ik-8