Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

TL;DR

This paper develops a method to simulate local excitations and evaluate non-equal-time correlators in iPEPS, enabling the study of hole dynamics in the t-J model with potential applications in quantum gas microscopy.

Contribution

The authors introduce auxiliary states in iPEPS to simulate local excitations and compute time-dependent correlators, overcoming previous limitations of the translationally-invariant ansatz.

Findings

Successfully simulated hole motion in the t-J model

Evaluated return probabilities and spin correlations

Method applicable to quantum gas microscope experiments

Abstract

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.