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arXiv:1911.02774 · Physical Review Research

Neural-network quantum states at finite temperature

Naoki Irikura, Hiroki Saito

Published Mar 9, 2020• 26 citations
arXivHTMLPDF

Abstract

The authors propose a variational method to obtain the finite temperature density matrix of a quantum many body system using a convolutional neural network with machine learning technique. This method is applied to the Bose-Hubbard model.
DOI
10.1103/physrevresearch.2.013284

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We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site occupation and the total energy, which is then minimized at the ground-state occupation. In contrast, at finite temperature the same relation is defined between the Helmholtz free energy and the equilibrium site occupation. Most importantly, both functionals are semilocal, so that they are independent from the size of the system under investigation and can be constructed over exact data for small systems. These ``exact'' functionals are numerically defined by neural networks. We also define additional neural networks for finite-temperature thermodynamical quantities, such as the entropy and heat capacity. These can be either a functional of the ground-state site occupation or of the finite-temperature equilibrium site occupation. In the first case their equilibrium value does not correspond to an extremal point of the functional, while it does in the second case. Our work gives us access to finite-temperature properties of many-body systems in the thermodynamic limit.