Local tensor network for strongly correlated projective states

TL;DR

This paper introduces a local Grassmann tensor network approach to efficiently encode and compute local operator averages for strongly correlated projective states, including fractional quantum Hall states.

Contribution

It provides an explicit construction of a local tensor network representation for strongly correlated projective states, enabling variational calculations with physically motivated trial wavefunctions.

Findings

Successfully encodes local operator averages in a Grassmann tensor network.

Enables the use of trial wavefunctions in tensor network variational methods.

Addresses the challenge of representing fractional quantum Hall states in tensor networks.

Abstract

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous efforts, strongly correlated projective states, fractional quantum Hall states in particular, have not yet found a local tensor network representation. Here we show that one can encode the calculation of averages of local operators in a Grassmann tensor network which is local. Our construction is explicit, and allows the use of physically motivated trial wavefunctions as starting points in tensor network variational calculations.