Quantum Scar States in Coupled Random Graph Models

Abstract

We analyze the Hilbert space connectivity of the $L$ site PXP-model by constructing the Hamiltonian matrices via a Gray code numbering of basis states. The matrices are all formed out of a single Hamiltonian-path backbone and entries on skew-diagonals. Starting from this observation, we construct an ensemble of related Hamiltonians based on random graphs with tunable constraint degree and variable network topology. We study the entanglement structure of their energy eigenstates and find two classes of weakly-entangled mid-spectrum states. The first class contains scars that are approximate products of eigenstates of the subsystems. Their origin can be traced to the near-orthogonality of random vectors in high-dimensional spaces. The second class of scars has $\log 2$ entanglement entropy and is tied to the occurrence of special types of subgraphs. The latter states have some resemblance to the Lin-Motrunich $\sqrt{2}$-scars.

discussion of experiments added; heuristic argument for boxed scars given; references added

References in corpus (10)

• Probing many-body dynamics on a 51-atom quantum simulator
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Quantum optimization with arbitrary connectivity using Rydberg atom arrays
• Solving Graph Problems Using Gaussian Boson Sampling
• Quantum simulation of Ising spins on Platonic graphs
• Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models

Cited by in corpus (2)

• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Weak ergodicity breaking transition in randomly constrained model