Machine learning approach to dynamical properties of quantum many-body systems

Article

关键词: MATRIX RENORMALIZATION-GROUP;    MONTE-CARLO;    ANALYTIC CONTINUATION;    MAXIMUM-ENTROPY;   

DOI  :  10.1103/PhysRevB.100.245123

来源: SCIE

【 摘 要 】

Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller-projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Green's function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional J(1) - J(2) Heisenberg model. The method is general and can be extended to other variational forms.

【 授权许可】

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