Gapless Hamiltonians for the toric code using the PEPS formalism

TL;DR

This paper introduces a method to construct gapless Hamiltonians sharing the toric code's ground state using PEPS, revealing continuous spectra in the thermodynamic limit for a broad class of 2D systems.

Contribution

It presents a novel PEPS-based construction of gapless Hamiltonians with the toric code ground state, expanding the understanding of topological phases and gapless excitations.

Findings

Constructed gapless Hamiltonians with the toric code ground state

Demonstrated continuous spectrum in the thermodynamic limit

Applicable to a broad class of 2D systems

Abstract

We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of Projected Entangled Pair States (PEPS), and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians".