Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations

• URL: http://arxiv.org/abs/2103.09469v1
• Date: Wed, 17 Mar 2021 07:00:29 GMT
• Title: Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• Authors: J. Koziol, A. Langheld, S.C. Kapfer, and K.P. Schmidt
• Abstract summary: The quantum-critical properties of the transverse-field Ising model are investigated by means of quantum Monte Carlo. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range universality classes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing auto-correlation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.

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