Auxiliary-field Monte Carlo for Quantum Spin and Boson Systems

Abstract

We describe a new algorithm for the numerical simulation of quantum spin and boson systems. The method is based on the Trotter decomposition in imaginary time and a decoupling by auxiliary Ising spins. It can be applied, in principle, to arbitrary (random) spin systems, however in general it suffers from the ``minus-sign problem''. This problem is absent in the case of the Ising model in a transverse field in arbitrary dimensions and geometries. We show test results for the spin--1/2 XY model, the one--dimensional transverse Ising model with disorder, and the phase transition induced by a transverse field in the two-dimensional Ising model.

7 pages, 4 figures

References in corpus (3)

• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains
• Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain

Cited by in corpus (3)

• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• Quantum Monte Carlo method for the ground state of many-boson systems
• Auxiliary-Field Monte Carlo for lattice bosons: tackling strong interactions and frustration