Interference-caged quantum many-body scars: a consequence of the Fock space topological localization

Tao-Lin Tan^1*, Yi-Ping Huang^1,2,3

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
²Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan
³Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Tao-Lin Tan, email:tanlin2013@gmail.com

The presence of athermal high-energy eigenstates in quantum many-body systems, known as quantum many-body scars, challenges the Eigenstate Thermalization Hypothesis. This article introduces a formulation of scars by interpreting the many-body Hilbert space as a Fock space graph, with a focus on closed quantum systems with weak ergodicity breaking. In this framework, scars emerge as localized eigenstates caged to specific subsets of vertices within the graph, where destructive interference of wavefunction amplitudes at their boundaries leads to anomalous thermal behavior. This phenomenon is analogous to compact localized states in flat-band physics. Due to the complexity of the graph, destructive interference is explained through Cauchy's eigenvalue interlacing theorem: the subgraph formed by these vertices coincidentally shares an eigenpair with the entire system only when precise cancellation occurs. This cancellation encodes a hidden symmetrical structure within the graph, making further analysis reliant on graph automorphisms a challenging task. Based on these insights, we propose algorithms to efficiently identify these subgraphs, enabling the computation of scars at a significantly lower computational cost compared to full exact diagonalization.

Keywords: Quantum many-body scars, Eigenstate Thermalization Hypothesis, Graph theory