Minimal model for Hilbert space fragmentation with local constraints

• URL: http://arxiv.org/abs/2106.14897v3
• Date: Mon, 11 Oct 2021 15:14:15 GMT
• Title: Minimal model for Hilbert space fragmentation with local constraints
• Authors: Bhaskar Mukherjee, Debasish Banerjee, K. Sengupta and Arnab Sen
• Abstract summary: We study a one-dimensional spin-$1/2$ lattice model with three-spin interactions in the same constrained Hilbert space. We show that this model possesses an extensive fragmentation of the Hilbert space which leads to a breakdown of thermalization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by previous works on a Floquet version of the PXP model [Mukherjee {\it et al.} Phys. Rev. B 102, 075123 (2020), Mukherjee {\it et al.} Phys. Rev. B 101, 245107 (2020)], we study a one-dimensional spin-$1/2$ lattice model with three-spin interactions in the same constrained Hilbert space (where all configurations with two adjacent $S^z=\uparrow$ spins are excluded). We show that this model possesses an extensive fragmentation of the Hilbert space which leads to a breakdown of thermalization upon unitary evolution starting from a large class of simple initial states. Despite the non-integrable nature of the Hamiltonian, many of its high-energy eigenstates admit a quasiparticle description. A class of these, which we dub as "bubble eigenstates", have integer eigenvalues (including mid-spectrum zero modes) and strictly localized quasiparticles while another class contains mobile quasiparticles leading to a dispersion in momentum space. Other anomalous eigenstates that arise due to a {\it secondary} fragmentation mechanism, including those that lead to flat bands in momentum space due to destructive quantum interference, are also discussed. The consequences of adding a (non-commuting) staggered magnetic field and a PXP term respectively to this model, where the former preserves the Hilbert space fragmentation while the latter destroys it, are discussed. A Floquet version with time-dependent staggered field also evades thermalization with additional features like freezing of exponentially many states at special drive frequencies. Finally, we map the model to a $U(1)$ lattice gauge theory coupled to dynamical fermions and discuss the interpretation of some of these anomalous states in this language. A class of gauge-invariant states show reduced mobility of the elementary charged excitations with only certain charge-neutral objects being mobile suggesting a connection to fractons.

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