Time evolution of an infinite projected entangled pair state: a neighborhood tensor update

TL;DR

This paper introduces the neighborhood tensor update (NTU), an intermediate method for time evolution in infinite projected entangled pair states (iPEPS), balancing accuracy and computational efficiency by considering nearest neighbor environments.

Contribution

The paper proposes NTU, a new tensor update algorithm for iPEPS that accounts for nearest neighbor environments, improving stability and accuracy over simple updates.

Findings

NTU yields stable unitary time evolution after a quench.

NTU accurately captures thermal states with large correlation lengths.

The method is computationally efficient and maintains Hermitian error measures.

Abstract

The simple update (SU) and full update (FU) are the two paradigmatic time evolution algorithms for a tensor network known as the infinite projected entangled pair state (iPEPS). They differ by an error measure that is either, respectively, local or takes into account full infinite tensor environment. In this paper we test an intermediate neighborhood tensor update (NTU) accounting for the nearest neighbor environment. This small environment can be contracted exactly in a parallelizable way. It provides an error measure that is Hermitian and non-negative down to machine precision. In the 2D quantum Ising model NTU is shown to yield stable unitary time evolution following a sudden quench. It also yields accurate thermal states despite correlation lengths that reach up to 20 lattice sites. The latter simulations were performed with a manifestly Hermitian purification of a thermal state. Both were performed with reduced tensors that do not include physical (and ancilla) indices. This modification naturally leads to two other schemes: a local SVD update (SVDU) and a full tensor update (FTU) being a variant of FU.