Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles

TL;DR

This paper introduces a variational algorithm for optimizing the time-evolved iPEPS in 2D quantum systems, enabling more accurate and efficient simulation of real and imaginary time evolution.

Contribution

It presents a novel variational method to optimize the evolved iPEPS, improving the representation of quantum states after time evolution.

Findings

Successfully simulates real time evolution in 2D quantum Ising model

Demonstrates imaginary time evolution of thermal states

Uses CTMRG for overlap computation

Abstract

A typical quantum state obeying the area law for entanglement on an infinite 2D lattice can be represented by a tensor network ansatz -- known as an infinite projected entangled pair state (iPEPS) -- with a finite bond dimension $D$. Its real/imaginary time evolution can be split into small time steps. An application of a time step generates a new iPEPS with a bond dimension $k$ times the original one. The new iPEPS does not make optimal use of its enlarged bond dimension $kD$, hence in principle it can be represented accurately by a more compact ansatz, favourably with the original $D$. In this work we show how the more compact iPEPS can be optimized variationally to maximize its overlap with the new iPEPS. To compute the overlap we use the corner transfer matrix renormalization group (CTMRG). By simulating sudden quench of the transverse field in the 2D quantum Ising model with the proposed algorithm, we provide a proof of principle that real time evolution can be simulated with iPEPS. A similar proof is provided in the same model for imaginary time evolution of purification of its thermal states.