Truncating loopy tensor networks by zero-mode gauge fixing

TL;DR

This paper introduces a novel method for truncating loopy tensor networks by using zero-mode gauge fixing to better handle loop correlations, improving initial truncation errors in tensor network compression.

Contribution

It proposes a new truncation technique leveraging zero modes of the metric tensor to enhance tensor network compression efficiency.

Findings

Better initial truncation errors than standard methods

Effective for infinite pair entangled projected states (iPEPS)

Applicable to periodic matrix product states (pMPS) in tensor renormalization group

Abstract

Loopy tensor networks have internal correlations that often make their compression inefficient. We show that even local bond optimization can make better use of the insight it has locally into relevant loop correlations. By cutting the bond, we define a set of states whose linear dependence can be used to truncate the bond dimension. The linear dependence is eliminated with zero modes of the states' metric tensor. The method is illustrated by a series of examples for the infinite pair entangled projected state (iPEPS) and for the periodic matrix product state (pMPS) that occurs in the tensor renormalization group (TRG) step. In all examples, it provides better initial truncation errors than standard initialization.