Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States

TL;DR

This paper develops local 2-body parent Hamiltonians for PEPS using perturbation gadgets, enabling efficient and stable realization of complex quantum states like topologically ordered states.

Contribution

It introduces a perturbative method to construct 2-body parent Hamiltonians for PEPS, including topologically ordered states, with explicit examples like the double semion string net.

Findings

Constructed 2-body parent Hamiltonians for PEPS.

Proved ground space stability for topologically ordered PEPS.

Explicit example for the double semion string net.

Abstract

We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. An encoded parent Hamiltonian for the double semion string net ground state is explicitly constructed as a concrete example.