Unstable periodic orbits galore and quantum hyperscarring in highly frustrated magnets

TL;DR

This paper uncovers a high-energy dynamical regime in frustrated magnets characterized by unstable periodic orbits and quantum hyperscarring, revealing coexistence of many-body chaos and structured coherent dynamics.

Contribution

It introduces the concept of unstable periodic orbits and hyperscarring in highly frustrated quantum magnets, a novel dynamical regime with extensive scarring phenomena.

Findings

Identification of an extensive manifold of unstable periodic orbits.

Observation of quantum hyperscarring on exponentially many unstable orbits.

Mid-spectrum eigenstates show power-law amplitude distribution, contrasting with Porter-Thomas distribution.

Abstract

Highly frustrated magnets, with their macroscopically-degenerate classical ground states and massively-entangled quantum spin liquid phases, have been pivotal to the development of modern condensed matter concepts such as emergent symmetries, topological order, and fractionalisation. The effects of frustration and massive degeneracies at high energy, where the many-body dynamics becomes chaotic, have hitherto been far less explored. Here, we identify a high-energy dynamical analog of highly-frustrated magnetism, in the form of an extensive manifold of classical ''interaction-suppressing'' configurations giving rise to unstable periodic orbits. These are in general neither protected by symmetry nor integrability, and emerge from a set of dynamical local constraints that effectively nullify the interactions while allowing extensively many local degrees of freedom. The proliferation of unstable periodic orbits corresponds in the quantum case to ''hyperscarring'', that is, quantum scarring on exponentially many unstable periodic orbits. On the product states associated to the latter, the amplitudes of the mid-spectrum thermal eigenstates exhibit a power-law distribution, in stark contrast to the expected exponential Porter-Thomas distribution that holds for generic product states. Our results reveal a new constrained dynamical regime where many-body quantum chaos coexists with structured manifolds of coherent dynamics, and establishes a mechanism for hitherto elusive extensive scarring.