Constructing exact representations of quantum many-body systems with deep neural networks

Giuseppe Carleo, Yusuke Nomura, Masatoshi Imada

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a constructive approach to generate artificial neural networks representing the exact ground states of a large class of many-body lattice Hamiltonians. It is based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations among physical degrees of freedom in the visible layer. The approach reproduces the exact imaginarytime Hamiltonian evolution, and is completely deterministic. In turn, compact and exact network representations for the ground states are obtained without stochastic optimization of the network parameters. The number of neurons grows linearly with the system size and total imaginary time, respectively. Physical quantities can be measured by sampling configurations of both physical and neuron degrees of freedom. We provide specific examples for the transverse-field Ising and Heisenberg models by implementing effcient sampling. As a compact, classical representation for many-body quantum systems, our approach is an alternative to the standard path integral, and it is potentially useful also to systematically improve on numerical approaches based on the restricted Boltzmann.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Feb 26
Externally publishedYes

ASJC Scopus subject areas

  • General

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