Matrix product state recursion methods for strongly correlated quantum systems

Abstract

We present a method for extrapolation of real-time dynamical correlation functions which can improve the capability of matrix product state methods to compute spectral functions. Unlike the widely used linear prediction method, which ignores the origin of the data being extrapolated, our recursion methods utilize a representation of the wavefunction in terms of an expansion of the same wavefunction and its translations at earlier times. This recursion method is exact for a noninteracting Fermi system. Surprisingly, the recursion method is also more robust than linear prediction at large interaction strength. We test this method on the Hubbard two-leg ladder, and present more accurate results for the spectral function than previous studies.

Machine Learning Regression for Operator Dynamics

“…By computing O using matrix product state (MPS) algorithms within the short-time domain, we shown that the longtime expectation values can be determined with low computational effort and good accuracy by utilizing a multi-layer perceptron (MLP) as a tool for linear regression. It is noted that previous extrapolation methods have been studied, but these have either focused on constructing the wave function at each increment of time 17 or implementing linear prediction methods to t-DMRG spectral calculations. 18 This paper is organized as follows: In Sec.…”