2018/07/23 by Tomotaka Kuwahara, Kuwahara, Tomotaka, Keiji Saito +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1807.08424
openalex publication_date 2018/07/23 · openalex created_date 2018/08/03 · openalex updated_date 2026/07/28
This paper discusses a classical simulation to compute the partition function (or free energy) of generic one-dimensional quantum many-body systems. Many numerical methods have previously been developed to approximately solve one-dimensional quantum systems. However, there exists no exact proof that arbitrary one-dimensional quantum Gibbs states can be efficiently solved by a classical computer. Therefore, the aim of this paper is to prove this with the clustering properties for arbitrary finite temperatures β-1. We explicitly show an efficient algorithm that approximates the partition function up to an error ε with a computational cost that scales as n⋅ \rm poly(1/ε), where the degree of the polynomial depends on β as eO(β). Extending the analysis to higher dimensions at high temperatures, we obtain a weaker result for the computational cost n⋅ (1/ε)^logD-1 (1/ε), where D is the lattice dimension.