Stochastic series expansion method for quantum Ising models with arbitrary interactions

Abstract

A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density matrix (stochastic series expansion), and avoids the interaction summations necessary in conventional methods. In the case of long-range interactions, the scaling of the computation time with the system size N is therefore reduced from N^2 to Nln(N). The method is tested on a one-dimensional ferromagnet in a transverse field, with interactions decaying as 1/r^2.

9 pages, 5 figures

References in corpus (15)

• Quantum Annealing in the Transverse Ising Model
• Simulated Tempering: A New Monte Carlo Scheme
• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• The Loop Algorithm
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Low temperature relaxational dynamics of the Ising chain in a transverse field
• Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Criticality in one dimension with inverse square-law potentials
• Universal, finite temperature, crossover functions of the quantum transition in the Ising chain in a transverse field
• Dynamics of the Ising Spin-Glass Model in a Transverse Field

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