Efficient approximation for global functions of matrix product operators

TL;DR

This paper introduces an efficient method to approximate global functions of matrix product operators, enabling the calculation of complex spectral quantities and thermal properties that are challenging for traditional tensor network approaches.

Contribution

It extends a block Lanczos method to efficiently approximate operator functions of MPOs, facilitating the computation of spectral and thermal properties.

Findings

Accurately computes von Neumann entropy and trace norm for MPOs.

Demonstrates improved efficiency in thermal property calculations.

Validates method with Lipkin-Meshkov-Glick and Ising models.

Abstract

Building on a previously introduced block Lanczos method, we demonstrate how to approximate any operator function of the form Trf (A) when the argument A is given as a Hermitian matrix product operator. This gives access to quantities that, depending on the full spectrum, are difficult to access for standard tensor network techniques, such as the von Neumann entropy and the trace norm of an MPO. We present a modified, more efficient strategy for computing thermal properties of short- or long-range Hamiltonians, and illustrate the performance of the method with numerical results for the thermal equilibrium states of the Lipkin-Meshkov-Glick and Ising Hamiltonians.