Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations

• URL: http://arxiv.org/abs/2403.05223v2
• Date: Wed, 5 Jun 2024 08:39:22 GMT
• Title: Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Authors: C. Krämer, J. A. Koziol, A. Langheld, M. Hörmann, K. P. Schmidt,
• Abstract summary: We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\nu_\mathrm{s}$ and $\nu_\mathrm{w}$ 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 $\beta$ and the critical exponent $\nu_{\mathrm{av}}$ 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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