Off-Diagonal Long-Range Order Implies Vanishing Charge Gap

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.

arXiv comment10 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

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