Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

TL;DR

This paper introduces a gradient tensor update method for simulating the time evolution of infinite 2D quantum lattice systems using iPEPS, optimizing truncation by directly maximizing overlap in tangent space.

Contribution

It proposes a novel gradient-based tensor update approach that improves truncation accuracy in iPEPS time evolution by operating in the tangent space of the variational manifold.

Findings

Benchmarking on 2D quantum Ising model shows improved accuracy.

Effectively captures quantum quench dynamics and Kibble-Zurek mechanism.

Outperforms traditional update methods in certain scenarios.

Abstract

Time evolution of an infinite 2D many body quantum lattice system can be described by the Suzuki-Trotter decomposition applied to the infinite projected entangled pair state (iPEPS). Each Trotter gate increases the bond dimension of the tensor network, $D$, that has to be truncated back in a way that minimizes a suitable error measure. This paper goes beyond simplified error measures -- like the one used in the full update (FU), the simple update (SU), and their intermediate neighborhood tensor update (NTU) -- and directly maximizes an overlap between the exact iPEPS with the increased bond dimension and the new iPEPS with the truncated one. The optimization is performed in a tangent space of the iPEPS variational manifold. This gradient tensor update (GTU) is benchmarked by a simulation of a sudden quench of a transverse field in the 2D quantum Ising model and the quantum Kibble-Zurek mechanism in the same 2D system.