  Hilbert space fragmentation (HSF) is a phenomenon that the Hilbert space of
an isolated quantum system splits into exponentially many disconnected
subsectors. The fragmented systems do not thermalize after long-time evolution
because the dynamics are restricted to a small subsector. Inspired by recent
developments of the HSF, we construct the Hamiltonian that exhibits the HSF in
the momentum space. We show that persistent-current (PC) states emerge due to
the HSF in the momentum space. We also investigate the stability of the PC
states against the random potential, which breaks the structure of the HSF, and
find that the decay rate of the PC is almost independent of the current
velocity.

Quantum Gases;Statistical Mechanics;Quantum Physics