Anomalous Eigenstates of a Doped Hole in the Ising Antiferromagnet

TL;DR

This paper uncovers anomalous, long-lived eigenstates in a simple model of a doped hole in an Ising antiferromagnet, revealing complex spectral features and slow thermalization linked to emergent local symmetries.

Contribution

It demonstrates the existence of anomalous eigenstates beyond the known spectrum in a doped Ising antiferromagnet, suggesting new quantum many-body scar states.

Findings

Identification of anomalous eigenstates with energies scaling linearly with J

Observation of avoided crossings with the ladder spectrum

Evidence of slow thermalization linked to emergent local C3 symmetry

Abstract

The problem of a mobile hole doped into an antiferromagnet Mott insulator is believed to underly the rich physics of several paradigmatic strongly correlated electron systems, ranging from heavy fermions to high-Tc superconductivity. Arguably the simplest incarnation of this problem corresponds to a doped Ising antiferromagnet, a problem widely considered essentially solved since almost 60 years by a popular yet approximate mapping to a single-particle problem on the Bethe lattice. Here we show that, despite its deceptive simplicity, the local spectrum of a single hole in a classical Ising-N\'eel state contains a series of anomalous, long-lived states that go beyond the well-known ladder-like spectrum with excited energies spaced as $J^{2/3} t^{1/3}$. The anomalous states we find through exact diagonalization and within the self-avoiding path approximation have excitation energies scaling approximately linear with $J$ and lead to a series of avoided crossings with the more pronounced ladder spectrum. By also computing different local, rotational spectra we explain the origin of the anomalous states as rooted in an approximate emergent local $C_3$ symmetry of the problem. From their direct spectral signatures we further conclude that these states lead to anomalously slow thermalization behavior -- hence representing a new type of quantum many-body scar state, potentially related to many-body scars predicted in lattice gauge theories.