Quantum Glass of Interacting Bosons with Off-Diagonal Disorder Has a Severe Sign Problem

A. Piekarska, T. Kopeć Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław 2, Poland

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We study a disordered system of interacting bosons, described by the Bose-Hubbard model with the disorder introduced via Gaussian-distributed hopping integrals. After applying the replica trick and the Trotter formula, we arrive at an expression for order parameters involving averaging with respect to the effective Hamiltonian, that has to be numerically evaluated. We show that the Monte Carlo algorithm fails because of the sign problem, which is severe in this case, hence cannot be removed via standard methods. It cannot be therefore excluded that this problem belongs to the NP-complete complexity class, i.e., of problems without known polynomial-time solution but with a possibility of validating a given solution candidate at such a computational complexity.

DOI:10.12693/APhysPolA.135.78 PACS numbers: 02.70.Tt, 05.30.Jp, 75.10.Nr, 67.85.Hj, 05.30.Rt