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arXiv · 2102.06111

Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains

Christopher M. Langlett·Shenglong Xu
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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.

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Christopher M. Langlett, Shenglong Xu. 2021-02-11. Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains. https://doi.org/10.1103/physrevb.103.l220304

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