The frustration-free fully packed loop model

TL;DR

This paper studies a quantum fully packed loop model with a frustration-free Hamiltonian, revealing exact eigenstates, entanglement properties, and a gapless spectrum in the thermodynamic limit.

Contribution

It introduces a boundary term that links ground state properties to combinatorics, classifies eigenstates, and demonstrates gapless behavior in the model.

Findings

Exact eigenstates are classified and constructed.

Ground state entanglement entropy follows area law.

The spectrum is gapless in the thermodynamic limit.

Abstract

We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. A boundary Hamiltonian is added to favour domain-wall boundary conditions and link ground state properties to the combinatorics and six-vertex model literature. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace, leading to a series of energy-equidistant exact eigenstates in the lower end of the spectrum. Among them we systematically classify both finitely entangled eigenstates and product eigenstates. Using a recursion relation for enumerating half-plane configurations, we compute numerically the exact entanglement entropy of the ground state, confirming area law scaling. Finally, the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.