Area-law entangled eigenstates from nullspaces of local Hamiltonians

TL;DR

This paper demonstrates that certain local Hamiltonians with nullspaces host zero-energy eigenstates exhibiting area-law entanglement, providing non-thermal eigenstates that challenge the eigenstate thermalization hypothesis.

Contribution

It introduces a method to identify and analyze zero-energy modes with area-law entanglement in local Hamiltonians, revealing non-thermal eigenstates.

Findings

Existence of zero modes represented as matrix product states.

Zero modes exhibit area-law entanglement scaling.

Zero modes break the strong thermalization hypothesis.

Abstract

Eigenstate thermalization in quantum many-body systems implies that eigenstates at high energy are similar to random vectors. Identifying systems where at least some eigenstates are non-thermal is an outstanding question. In this work we show that interacting quantum models that have a nullspace -- a degenerate subspace of eigenstates at zero energy (zero modes), which corresponds to infinite temperature, provide a route to non-thermal eigenstates. We analytically show the existence of a zero mode which can be represented as a matrix product state for a certain class of local Hamiltonians. In the more general case we use a subspace disentangling algorithm to generate an orthogonal basis of zero modes characterized by increasing entanglement entropy. We show evidence for an area-law entanglement scaling of the least entangled zero mode in the broad parameter regime, leading to a conjecture that all local Hamiltonians with the nullspace feature zero modes with area-law entanglement scaling, and as such, break the strong thermalization hypothesis. Finally, we find zero-modes in constrained models and propose setup for observing their experimental signatures.