Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains

TL;DR

This paper introduces a family of spin-1/2 Hamiltonians based on the Fredkin chain, exhibiting Hilbert space fragmentation and quantum many-body scars, leading to non-ergodic dynamics demonstrated through analytical constructions and numerical simulations.

Contribution

It presents a novel class of Hamiltonians with Hilbert space fragmentation and exact scar states, connecting kinetic constraints to non-ergodic behavior in quantum many-body systems.

Findings

Existence of exact eigenstates with low entanglement in fragmented sectors

Demonstration of tunable non-ergodic dynamics via quench simulations

Development of a Floquet circuit sharing the same fragmentation and scarring features

Abstract

In this work, based on the Fredkin spin chain, we introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the 1D Fermi-Hubbard model in the infinite onsite repulsion limit. To demonstrate the many-body scars, we construct an exact eigenstate that is in the middle of the spectrum within each fractured sub-sector displaying either logarithmic or area-law entanglement entropy. The interplay between fragmentation and scarring leads to rich tunable non-ergodic dynamics by quenching different initial states that is shown through large scale matrix product state simulations. In addition, we provide a Floquet quantum circuit that displays non-ergodic dynamics as a result of sharing the same fragmentation structure and scarring as the Hamiltonian.