Stochastic series expansion method for quantum Ising models with arbitrary interactions

2003/03/29 by Anders W. Sandvik · 7 citations
Physics and Astronomy · #Opinion Dynamics and Social Influence #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.68.056701

published as Phys. Rev. E 68, 056701 (2003) · 9 pages, 5 figures

arxiv created 2003/03/29 · openalex publication_date 2003/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 N2 to N ln(N). The method is tested on a one-dimensional ferromagnet in a transverse field, with interactions decaying as 1/r(2).

Citations

• Quantum annealing in the transverse Ising model
• A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model

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• Qubit encodings for lattices of dipolar planar rotors
• Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography
• Eigenstate Thermalization and Spontaneous Symmetry Breaking in the One-Dimensional Transverse-Field Ising Model with Power-Law Interactions

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