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arXiv:2609.06515

Superfluidity in active quantum flocks

Byjesh N. Radhakrishnan, Reyhaneh Khasseh, Thomas Schmidt, Markus Heyl

cond-mat.quant-gasphysics.bio-phquant-phSubmitted Sep 6, 2026• Announced Sep 8, 2026• 0 citations• Revised Sep 9, 2026 (v2)
v1 · Sep 6, 2026v2 · Sep 9, 2026
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Abstract

Active quantum matter has very recently emerged at the intersection between bio- and quantum many-body physics, combining the self-organization of living systems with the coherence of the quantum world. Active quantum systems have been shown to exhibit flocking - a collective phenomenon with no precedent in equilibrium quantum physics. In this work we uncover an unexpected layer of quantum order in active quantum flocks: they can become superfluid. We show that, in addition to the symmetry breaking associated with their directed motion, these flocks can also break an additional U(1) symmetry, giving rise to off-diagonal long-range order. For a microscopic model of active hard-core bosons governed by Lindblad dynamics, we derive an effective long-wavelength description of the single-particle density matrix and demonstrate that the flocking phase develops an instability toward off-diagonal long-range order characteristic of superfluid behavior. Our findings reveal active quantum matter as a promising research direction for discovering exotic nonequilibrium phases of quantum matter.

Comments
Combined main manuscript and supplementary material

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Active quantum matter has very recently emerged at the intersection between bio- and quantum many-body physics, combining the self-organization of living systems with the coherence of the quantum world. Active quantum systems have been shown to exhibit flocking - a collective phenomenon with no precedent in equilibrium quantum physics. In this work we uncover an unexpected layer of quantum order in active quantum flocks: they can become superfluid. We show that, in addition to the symmetry breaking associated with their directed motion, these flocks can also break an additional U(1) symmetry, giving rise to off-diagonal long-range order. For a microscopic model of active hard-core bosons governed by Lindblad dynamics, we derive an effective long-wavelength description of the single-particle density matrix and demonstrate that the flocking phase develops an instability toward off-diagonal long-range order characteristic of superfluid behavior. Our findings reveal active quantum matter as a promising research direction for discovering exotic nonequilibrium phases of quantum matter.
Flocks of animals represent a prominent archetype of collective behavior in the macroscopic classical world, where the constituents, such as birds, concertedly perform motions and actions as if being one single entity. Here, we address the so far open question of whether flocks can also form in the microscopic world at the quantum level. For that purpose, we introduce the concept of active quantum matter by formulating a class of models of active quantum particles on a one-dimensional lattice. We provide both analytical and large-scale numerical evidence that these systems can give rise to quantum flocks. A key finding is that these quantum flocks exhibit distinct quantum properties by developing strong quantum coherence over long distances. We propose that quantum flocks could be experimentally observed in Rydberg atom arrays.
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.
We propose a quantum model consisting of an ensemble of overdamped spin−1/2-1/2−1/2 particles with ferromagnetic couplings, driven by a radially homogeneous magnetic field. The spontaneous magnetization of the spin components breaks the SO(3)SO(3)SO(3) (or SO(2)SO(2)SO(2)) symmetry, inducing an ordered phase of flocking. Our model converges to the Vicsek model in the classical limit and corresponds to the Toner-Tu model in the continuous limit. Our investigation not only elucidates the intrinsic connection between these two models, but also introduces new opportunities for exploring the mechanisms underlying flocking order and correlations at the quantum level, which maybe pave the way for a new field of research -- the quantum active matter.
We study the quantum dynamics of superfluids of bosons hybridized with Cooper pairs near Feshbach resonances and the influence of fermion–boson conversion on Mott states. We derive a set of equations of motion which describe novel low energy dynamics in superfluids and obtain a new distinct branch of gapped collective modes in superfluids which involve anti-symmetric phase oscillations in fermionic and bosonic channels. We also find that Mott states in general are unstable with respect to fermion–boson conversion; particles become delocalized and the off-diagonal long-range order of superfluids can be developed when a finite conversion is present. We further point out a possible hidden order in Mott states. It is shown that the quantum dynamics of Fermi–Bose states can be characterized by either an effective coupled U (1) ⊗ U (1) quantum rotor Hamiltonian in a large- N limit or a coupled XXZ ⊗ XXZ spin Hamiltonian in a single-orbit limit.
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Non-equilibrium quantum many-body systems have attracted considerable attention in the past decades. The scope of the research of this kind of novel system involves interdisciplinary research of condensed matter, atomic and molecular physics, quantum optics, quantum information and quantum computation, as well as the non-equilibrium statistical physics. The non-equilibrium phenomena emerging from the aforementioned quantum systems can exhibit rich and universal behaviors, which have far from being well understood due to the novelties and complexities of these systems, and hence the quantum many-body physics becomes the research highlight. At the same time, with the rapid development of quantum techniques, the understanding of these complex systems is of important practical significance due to their potential applications in quantum computation and quantum manipulation. In this paper, we show our recent progress of non-equilibrium quantum many-body systems. We focus on the novel phenomena closely related to the temporary symmetry breaking, including the exotic quantum matter, quasi-particles as well as the dynamical universality classes in non-equilibrium quantum many-body systems.