Off-Diagonal Long-Range Order Implies Vanishing Charge Gap

Hal Tasaki; Haruki Watanabe

doi:10.1103/physrevb.104.l180501

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arXiv · 2105.10692

Off-Diagonal Long-Range Order Implies Vanishing Charge Gap

Hal Tasaki·Haruki Watanabe

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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.

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Hal Tasaki, Haruki Watanabe. 2021-05-22. Off-Diagonal Long-Range Order Implies Vanishing Charge Gap. https://doi.org/10.1103/physrevb.104.l180501

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