Activity-induced ferromagnetism in one-dimensional quantum many-body systems

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