Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs

TL;DR

This paper constructs exactly solvable pseudo-Hermitian 2D spin Hamiltonians whose ground states are characterized by non-semisimple TQFTs, extending topological quantum field theory models to new algebraic settings.

Contribution

It introduces a class of pseudo-Hermitian Hamiltonians linked to non-semisimple TQFTs, broadening the scope of topological quantum models.

Findings

Ground states depend only on surface topology

Ground state values are given by non-semisimple TQFTs

Example from quantum sl(2) subcategory at root of unity

Abstract

We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value assigned to the surface by a non-semisimple TQFT generalizing the Turaev-Viro model. A non-trivial example arises from a non-semisimple subcategory of representations of quantum sl(2) where the quantum parameter is specialized to a root of unity.