Variational Neural and Tensor Network Approximations of Thermal States

• URL: http://arxiv.org/abs/2401.14243v2
• Date: Tue, 28 Jan 2025 15:58:35 GMT
• Title: Variational Neural and Tensor Network Approximations of Thermal States
• Authors: Sirui Lu, Giacomo Giudice, J. Ignacio Cirac,
• Abstract summary: We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems. We employ a variety of trial states -- both tensor networks as well as neural networks -- as variational Ans"atze for our numerical optimization.
• Score: 0.3277163122167433
• License:
• Abstract: We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the ansatz expressiveness without accumulating errors from iterative imaginary time evolution. We employ a variety of trial states -- both tensor networks as well as neural networks -- as variational Ans\"atze for our numerical optimization. We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to $N=100$ spins. Our results demonstrate that while restricted Boltzmann machines show limitations, string bond tensor network states exhibit systematic improvements with increasing bond dimensions and the number of strings.

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