Extracting conserved operators from a projected entangled pair state

TL;DR

This paper introduces a method to extract conserved operators, including Hamiltonians, from a given tensor network state, enabling the identification of local Hamiltonians with specific eigenstates in 2D systems.

Contribution

The authors present a novel approach to determine geometrically local conserved operators for tensor network states, improving upon standard methods and capturing non-frustration-free Hamiltonians.

Findings

Successfully extracted frustration-free and non-frustration-free Hamiltonians from iPEPS.

Identified a 4-site-plaquette Hamiltonian with the short-range RVB state as ground state.

Discovered a Hamiltonian where the deformed toric code state is an excited eigenstate, indicating quantum many-body scars.

Abstract

Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically $k$-local conserved operators that have the given infinite projected entangled pair state (iPEPS) in 2D as an (approximate) eigenstate. The key ingredient is the evaluation of the static structure factors of multi-site operators through differentiating the generating function. These generating functions define a manifold of the given tensor network state deformed by some parameters, endowed with a quantum geometry, where conserved operators correspond to vanishing fidelity susceptibility. Despite the approximation errors, we show that our method is still able to extract from exact or variational iPEPS to good precision both frustration-free and non-frustration-free parent Hamiltonians that are beyond the standard construction and obtain better locality. In particular, we find a 4-site-plaquette local Hamiltonian that approximately has the short-range RVB state as the ground state. Moreover, we find a Hamiltonian for which the deformed toric code state at arbitrary string tension is an excited eigenstate with the same energy, thereby potentially realizing quantum many-body scars.