2018/08/29 by Manaka Okuyama, Masayuki Ohzeki, Okuyama, Manaka +1
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #FOS: Physical sciences #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.48550/arxiv.1808.09707
13 pages, 0 figure
arxiv created 2018/08/29 · openalex publication_date 2018/08/29 · arxiv updated 2018/08/30 · openalex created_date 2018/09/07 · openalex updated_date 2026/07/28
Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to explicitly treat the imaginary-time dependence of the partition function, we usually neglect the imaginary-time dynamical effect, which is called the static approximation. Although the static approximation is the first approach, it is not even clear when the static approximation is justified for mean-field quantum spin systems, that is, mean-field quantum spin systems have not been solved exactly so far. In this study, we solve exactly the partition function for a particular class of mean-field quantum spin systems including randomness without the static approximation. The partition function can be regarded as a result of time evolution in the imaginary-time Schrödinger equation, and solving the exact solution of the partition function is equivalent to solving the optimal control problem in the imaginary-time Schrödinger equation. As the result, the solution of the optimal control problem coincides exactly with the static approximate solution of the partition function and, therefore, the static approximation is exact for the particular class of mean-field quantum spin systems including randomness in general. Furthermore, we prove that the analysis of the previous study in quantum annealing is exact where the non-stoquastic interaction and the inhomogeneous transverse field accelerate the computational time exponentially for mean-field quantum spin systems.