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Off-Diagonal Long-Range Order Implies Vanishing Charge Gap (2105.10692v3)
Published 22 May 2021 in cond-mat.quant-gas, cond-mat.stat-mech, cond-mat.str-el, cond-mat.supr-con, and quant-ph
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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