Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
arxiv(2024)
摘要
We study the ferromagnetic transverse-field Ising model with quenched
disorder at T = 0 in one and two dimensions by means of stochastic series
expansion quantum Monte Carlo simulations using a rigorous zero-temperature
scheme. Using a sample-replication method and averaged Binder ratios, we
determine the critical shift and width exponents ν_s and
ν_w as well as unbiased critical points by finite-size scaling.
Further, scaling of the disorder-averaged magnetisation at the critical point
is used to determine the order-parameter critical exponent β and the
critical exponent ν_av of the average correlation length. The
dynamic scaling in the Griffiths phase is investigated by measuring the local
susceptibility in the disordered phase and the dynamic exponent z' is
extracted. By applying various finite-size scaling protocols, we provide an
extensive and comprehensive comparison between the different approaches on
equal footing. The emphasis on effective zero-temperature simulations resolves
several inconsistencies in existing literature.
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