Collective Behaviour of a Boson System

Xiao-Gang Wen

Jean G. Valatin

Kian L. Assent, Emil Strauch, Sabine H. L. Klapp +2 more

Collective behaviour such as flocking (the collective motion of a spontaneously formed group along a common direction) or aster formation (the binding of opposing flocks, inhibiting each others motion) are intriguing emergent phenomena in active systems with local alignment rules. Until recently, their occurrence was mainly studied for classical systems, a prime example being the active Ising model (AIM), which translates the main ingredients of flocking and aster formation (i.e., alignment and self-propulsion) to a lattice framework. Here we introduce and study a one-dimensional (1D) quantum lattice variant of the AIM, based on ideal bosons with a spin degree of freedom. We find that both the collective behaviours of the 1D classical model, flocking and aster formation, are markedly enhanced by the bosonic quantum statistics. This contrasts with a recent quantum generalization of the AIM based onto hard-core bosons [Khasseh et al., Phys. Rev. Lett. 135, 248302 (2025)], where flocking, but neither its quantum-statistical stabilization nor aster states were observed as a consequence of interactions. Moreover, we investigate the competition of this quantum statistical stabilization of collective phases with their suppression by the quantum fluctuations induced by a transverse external magnetic field.

Mitchell J. Knight, Harry M. Quiney, Andy M. Martin

The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of N N harmonically trapped bosons interacting via contact interaction, where N N ranges from 2 2 to 10^4 10 4 . The ground-state energies are calculated, and compared to existing methods, including the analytic case (for N=2) N = 2 ) and mean-field approaches such as the one-dimensional Gross-Pitaevskii equation and its variations. Structural properties such as the density and correlation functions are also derived, including the behaviour of the correlation function when boson coordinates coincide. This collectively demonstrates the capacity of the reduced density matrix method to accurately calculate collective ground-state properties of bosonic systems comprising few to many bosons, including the cross-over region between these extremes, across a large range of interaction strengths.