Active matter, an ensemble of self-propelled entities, exhibits various
nonequilibrium phase transitions. Here we construct a non-Hermitian quantum
many-body model in one dimension analogous to the Vicsek model, and investigate
its quantum phase transitions. The model consists of two-component hard-core
bosons with ferromagnetic interactions and activity, i.e., spin-dependent
asymmetric hopping. Numerical results show the emergence of a ferromagnetic
order induced by the activity, a quantum counterpart of flocking, that even
survives without the ferromagnetic interaction. We prove that activity
generally increases the ground state energies of the paramagnetic states,
whereas the ground state energy of the ferromagnetic state does not change. By
solving the two-particle case, we find that this effective alignment is caused
by avoiding the bound state formation due to the non-Hermitian skin effect in
the paramagnetic state. To take this effect into account, we employ a two-site
mean-field theory and qualitatively reproduce the phase diagram. We further
numerically study a variant of our model, where the hard-core condition is
relaxed, and confirm the robustness of the ferromagnetic order.Comment: 13 pages, 8 figures, the first two authors contributed equally; v2:
nonperturbative proof of the ferromagnetic ground state; v3: updated abstrac