Off-Diagonal Long-Range Order Implies Vanishing Charge Gap

TL;DR

This paper proves a general inequality linking off-diagonal long-range order with the charge gap in quantum many-body systems, showing that such order implies a vanishing charge gap and nonzero charge susceptibility.

Contribution

It establishes a universal inequality connecting long-range order and the charge gap, providing new insights into the properties of quantum many-body ground states.

Findings

Ground states with off-diagonal long-range order have zero charge gap.

In quantum spin systems, magnetization plateaus cannot host transverse long-range order.

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.