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Hilbert space fragmentation (HSF) is a phenomenon that the Hilbert space ofan isolated quantum system splits into exponentially many disconnectedsubsectors. The fragmented systems do not thermalize after long-time evolutionbecause the dynamics are restricted to a small subsector. Inspired by recentdevelopments of the HSF, we construct the Hamiltonian that exhibits the HSF inthe momentum space. We show that persistent-current (PC) states emerge due tothe HSF in the momentum space. We also investigate the stability of the PCstates against the random potential, which breaks the structure of the HSF, andfind that the decay rate of the PC is almost independent of the currentvelocity.

Persistent-current states originating from the Hilbert space fragmentation in momentum space