For a large class of quantum many-body systems with U(1) symmetry, we prove general inequality that relates the (off-diagonal) long-range order charge gap. system bosons or fermions on lattice in continuum, implies ground state off-diagonal inevitably has vanishing gap, and hence is characterized by nonzero susceptibility. spin system, within magnetization plateau cannot have transverse order.

Thermodynamically driven short-range order (SRO) is known to exist in multi-component alloys and can influence their mechanical properties. Atomistic mesoscale simulations are frequently used study the effects of SRO, but introducing SRO into lattice usually requires costly Monte Carlo simulations. Here, we develop a novel method open-source code create lattices with specified parameters that b...