Exact Valence-Bond Solid Scars in the Square-Lattice Heisenberg Model

TL;DR

This paper discovers exact many-body scar states in the square-lattice Heisenberg model, revealing simple valence-bond solid states with zero energy that challenge typical thermalization expectations.

Contribution

It identifies and characterizes exact valence-bond solid scars in the Heisenberg model, a novel finding in quantum many-body physics.

Findings

Valence-bond solid scars are exact zero-energy eigenstates.

Scars exist in even-by-even systems and width-2 ladders.

These scars dominate the spectrum, nearly exhausting all eigenstates.

Abstract

We show that the spin-s square-lattice Heisenberg model has exact many-body scars. These scars are simple valence-bond solids with exactly zero energy, and they exist in even-by-even systems and ladders of width 2. Ladders have additional scars corresponding to injecting one or two magnons on top of a parent valence-bond solid scar. These scars have a remarkably simple physical origin based only the angular momentum algebra and cancellations from spin-antialignment within a valence bond. Our comprehensive exact diagonalization calculations suggest that our valence-bond solids exhaust all exact eigenstates in the Heisenberg model except for few-magnon states near the top of the spectrum. Our scars are interesting because they are not part of a tower, have area-law entanglement, break translation symmetry, and exist for Heisenberg models of all spin.