Spectral functions with infinite projected entangled-pair states

TL;DR

This paper introduces a method to compute spectral functions in two-dimensional strongly correlated systems using infinite projected entangled-pair states (iPEPS), enabling efficient evaluation of non-equal time correlators in the thermodynamic limit.

Contribution

The authors extend iPEPS techniques by developing a method to evaluate spectral functions through real-time evolution of ground states with operator insertions, improving the analysis of dynamical properties.

Findings

Spectral functions can be computed efficiently with small bond dimensions.

Main features of the dynamical structure factor are accurately reproduced.

Magnon dispersion results agree well with previous iPEPS excitation data.

Abstract

Infinite projected entangled-pair states (iPEPS) provide a powerful tool to study two-dimensional strongly correlated systems directly in the thermodynamic limit. In this work, we extend the iPEPS toolbox by a method to efficiently evaluate non-equal time two-point correlators, enabling the computation of spectral functions. It is based on an iPEPS ansatz of the ground state in a large unit cell, with an operator applied in the center of the cell, which is evolved in real-time using the fast-full update method. At every time step, the two-point correlators within a cell are computed based on the corner transfer matrix renormalization group method. Benchmark results for the 2D transverse field Ising model show that the main features of the dynamical structure factor can already be reproduced at relatively small bond dimensions and unit cell sizes. The results for the magnon dispersion are found to be in good agreement with previous data obtained with the iPEPS excitation ansatz.