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

TL;DR

This paper investigates a one-dimensional non-Hermitian quantum many-body model showing that activity induces ferromagnetic order, even without ferromagnetic interactions, revealing a quantum analog of flocking behavior.

Contribution

It introduces a non-Hermitian quantum model demonstrating activity-induced ferromagnetism and provides analytical and numerical evidence for this novel phase transition.

Findings

Activity induces ferromagnetic order in the model.

Ferromagnetic order persists without ferromagnetic interactions.

The phenomenon is robust under model variations.

Abstract

We study a non-Hermitian quantum many-body model in one dimension analogous to the Vicsek model or active spin models, 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 in the absence of ferromagnetic interaction. We confirm this phenomenon by proving 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 the effective alignment is caused by avoiding the bound state formation due to the non-Hermitian skin effect in the paramagnetic state. We employ a two-site mean-field theory based on the two-particle result and qualitatively reproduce the phase diagram. We further numerically study a variant of our model with the hard-core condition relaxed, and confirm the robustness of ferromagnetic order emerging due to activity.