# Time-dependent study of disordered models with infinite projected entangled pair states

## TL;DR

This paper demonstrates the use of infinite projected entangled pair states (iPEPS) for simulating real-time dynamics and disorder effects in two-dimensional quantum systems, enabling new insights into their behavior.

## Contribution

It introduces a method for real-time evolution and disorder-averaging in iPEPS, expanding the capabilities of tensor network simulations for disordered quantum systems.

## Key findings

- Successfully simulated short-time dynamics of the Heisenberg model with disorder
- Showed feasibility of real-time evolution in iPEPS for disordered systems
- Applied disorder-averaging to maintain translational invariance

## Abstract

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field.