A tensor network approach to 2D bosonization

TL;DR

This paper introduces a tensor network operator that achieves exact 2D bosonization at the quantum state level, enabling explicit algorithms for bosonizing fermionic states on arbitrary 2D manifolds.

Contribution

It develops a tensor network-based duality for 2D bosonization, allowing bosonization of quantum states and fermionic PEPS with explicit algorithms.

Findings

Constructed an exact tensor network operator for 2D bosonization.

Enabled bosonization of fermionic PEPS using the tensor network approach.

Applicable to systems on arbitrary triangulations of 2D manifolds.

Abstract

We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for bosonization at the level of quantum states. Thus, we use the TNO to provide an explicit algorithm for bosonizing fermionic projected entangled pair states (fPEPs). A key step in the algorithm is to account for a choice of spin-structure, encoded in a set of bonds of the bosonized fPEPS. This enables our tensor network approach to bosonization to be applied to systems on arbitrary triangulations of orientable 2D manifolds.