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.
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.
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.
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. Published by the American Physical Society 2024
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.
A team at the University of Augsburg in Germany, working with a colleague based in Barcelona and Dresden, used a one-dimensional hard-core boson lattice model to present compelling numerical evidence for a quantum version of motility-induced phase separation (MIPS), the clustering that active particles undergo without any attraction between them. The minimal model produced giant number fluctuations but settled into microphase separation, many finite clusters rather than a single macroscopic domain; adding a repulsive interaction between neighbouring particles yielded a characteristic length that grows strongly with system size, which the researchers read as consistent with genuine phase separation. Most strikingly, inside a dense cluster the exclusion constraint blocks most dissipative hops, leaving long-distance quantum coherence intact and suggesting that activity and quantum behaviour can cooperate rather than compete in producing a new kind of nonequilibrium state. [Quantum Biology Society] In active matter systems such as bacterial colonies and self-propelled colloids, particles slow down as the local density rises, which causes further accumulation and further slowing, until the system spontaneously separates into a dense phase and a dilute one. This is motility-induced phase separation (MIPS), and it happens with no attractive force between the particles at all. Physicists have recently begun carrying active matter concepts over into the quantum world, but MIPS itself, the other cornerstone of the field alongside flocking, had remained unexplored in the quantum regime. A preprint posted to arXiv in August 2026 by researchers in Germany and Spain, with Laurin Brunner and Markus Heyl of the University of Augsburg as corresponding authors, reports numerical evidence for quantum MIPS in a one-dimensional open quantum system. One note for readers of the archive: this paper is not about a living system. It is a pure quantum many-body simulation of a lattice model whose ingredients are, in principle, within reach of ultracold atomic and Rydberg platforms. ■ A one-dimensional hard-core boson lattice: fusing activity with quantum dynamics The model is a chain of L sites with periodic boundary conditions, filled to half density with hard-core bosons. Infinite on-site repulsion, imposed across spin species as well, allows at most one particle per site whatever its internal state, and each particle carries an internal spin pointing left or right. The density matrix evolves under a Lindblad master equation, and two processes compete inside it. Dissipative run: asymmetric quantum jump operators move a particle only in the direction its internal spin points, and only if the target site is empty. Because this dissipative dynamics breaks local detailed balance, the system counts as active. Coherent tumble: the Hamiltonian coherently rotates the internal spin, turning left into right and back. This is the quantum stand-in for the random reorientation of classical run-and-tumble motion, with one difference the researchers highlight. The quantum flip probability follows sin²(gt/ℏ), so it grows quadratically at short times through Rabi oscillations rather than linearly as classical tumbling does. They read this as a hint that quantum properties might enhance the effective persistence length and strengthen the tendency to cluster. Two structural features made large simulations possible. The effective Hamiltonian commutes with the local occupation operators, so the spatial arrangement of particles stays fixed between quantum jumps, which cuts the Hilbert space from 3^L down to 2^N. In the minimal model the state factorises further into independent single-site contributions, leaving only 2N complex numbers to track. Using the Monte Carlo wave-function method, the team ran numerically exact simulations up to L = 1000 lattice sites. ■ Giant number fluctuations, microphase separation, and the addition of repulsion A hallmark of MIPS is giant number fluctuations, meaning the variance of the particle number in a subsystem grows faster than its mean. Microphase separation (minimal model): at weak quantum amplitude (g/ℏγ = 0.05) the fluctuations scaled superlinearly with an exponent of β ≈ 1.7, the signature of strong clustering. The characteristic length scale, however, grew with system size only very slowly, more slowly than logarithmically, and slowly enough that the researchers cannot rule out convergence to a finite value in the infinite-size limit. Only in the singular limit of vanishing quantum amplitude did they find evidence for a diverging length. The weak-g steady state is therefore best described as microphase separation: many dense clusters of finite size rather than one macroscopic domain. Genuine phase separation (extended model): to push past that, the researchers added a repulsive interaction between neighbouring particles of the same spin. The term penalises locally aligned motility states and favours neighbouring spins pointing opposite ways. Of the two anti-aligned arrangements, the one in which the spins point away from each other does not last, since motility simply carries the particles apart; the only long-lived arrangement has the spins pointing toward each other, which is exactly the self-trapping that underlies MIPS. With this term added, the characteristic length grew strongly with system size and approached the upper bound a maximally clustered state would set, and at g/ℏγ = 0.1 the particles condensed into a single dense cluster. The researchers treat this as consistent with genuine phase separation rather than as proof of it. The interaction also breaks the exact factorization, confining these simulations to roughly 30 sites, too few for a reliable number-fluctuation scaling test, so the characteristic length had to carry the argument alone. The paper also notes an earlier proposal that a quantum analogue of MIPS could be realised in the ground state of a non-Hermitian Hamiltonian. Since it remains unclear whether such ground states can be produced experimentally, the researchers present their Lindblad setting as the first realistic one for an actual quantum MIPS phase. ■ Clustering that shelters quantum coherence The most striking result concerns what the dissipation does to quantum coherence. The natural expectation is that the dissipative dynamics driving the clustering would destroy it. The opposite happened. The mechanism is straightforward. The dissipative channel is the quantum jump that carries a particle into an empty neighbouring site. Inside a dense cluster there are almost no empty sites to jump into, so the exclusion constraint blocks most hops and the dissipative dynamics goes largely idle. That leaves the unitary spin dynamics free to generate superpositions, precisely in the regime where clustering is strongest. As the researchers put it, the clustering itself creates a protected environment for coherence. Measured with the ℓ₁ coherence of the two-site reduced density matrix at L = 20, nearest-neighbour coherence was finite across every parameter tested. Longer-range coherence depended strongly on the quantum amplitude: at weak amplitudes it stayed sizeable out to a separation of about seven sites, while at strong amplitudes it decayed beyond two. Adding the repulsive interaction slightly suppressed nearest-neighbour coherence but made coherence at large separations more robust. One distinction is worth keeping straight. In the minimal model the factorised wave function rules out spatial entanglement between sites by construction; the steady state is a classical mixture of product states that is nonetheless genuinely quantum, which is why the researchers identify coherence, rather than entanglement, as the relevant quantum signature. In the extended model the factorization breaks down and spatial entanglement does appear, over a narrow window of quantum amplitude. Both models show small but finite entanglement between the two spin species. ■ Significance and limits The work amounts to a numerical existence argument. MIPS, long the property of classical statistical physics, can be reproduced inside a one-dimensional quantum many-body system, and the clustered steady state there is not a classical phase-separated mixture but an inherently quantum one. The authors are candid about what has not been shown. Nothing here was observed in a laboratory. The macroscopic phase separation rests on simulations of roughly thirty lattice sites, and in the minimal model the extrapolation of the characteristic length remains genuinely ambiguous. Everything is one-dimensional. In the coherence calculations, convergence in the number of trajectories could not be confirmed at larger quantum amplitudes and longer distances, so those values are treated as upper bound estimates. What the framework does offer is a concrete target. The ingredients the model needs, engineered directed dissipation, coherent spin rotation and hard-core constraints, are in principle within reach of ultracold quantum gases and Rydberg atom arrays. That makes quantum MIPS something an experiment could go looking for, and positions active quantum matter as a setting in which coherence is not a passive bystander but a participant. #QuantumBiology #ActiveMatter #MotilityInducedPhaseSeparation #MIPS #QuantumCoherence #Lindblad #NonequilibriumQuantumPhases #HardCoreBosons #UltracoldAtoms #RydbergAtoms #Preprint https://arxiv.org/abs/2608.25649
Bosonic excitations within long-range ordered, but strongly inhomogeneous phases have been studied in quite some detail. My thesis focuses instead on understanding the insulating, localized phase of disordered bosonic systems. In particular I study localization properties of strongly interacting bosons and spin systems in a disorder potential at zero temperature. I focus on simple, prototypical spin models (Ising model and XY model) in random fields on a Cayley tree with large connectivity. Regarding the nature of the quantum phase transition in strong disorder I find the following results: i) With a uniformly distributed disorder non-extensive excitations in the disordered phase are all localized. ii)Moreover, I find that the order arises due to a collective condensation, which is qualitatively distinct from a Bose Einstein condensation of single particle excitations into a delocalized state. In particular, in non-frustrated Bose glasses, I do not find evidence for a boson mobility edge in the Bose glass. These results are qualitatively different from claims in the recent literatures . Considering that (many body) localization of bosons is a kind of quantum glass transition, it is an interesting question to ask what phenomena occur, if the ingredients for more conventional (classical) glassy physics are added to a disordered bosons system, namely: random, frustrated interactions between the bosons. One can still think about such a system as bosons in a disordered potential, where the disordered potential is, at least partly, self-generated by random frustrated interactions between the bosons. This question takes us to the study of another type of disordered systems: glassy systems. Those are typically characterized by low temperature phases with an inhomogeneous density or magnetization pattern, which is extremely long-lived due to the occurrence of non-trivial ergodicity breaking. I study a solvable model of hard core bosons (pseudospins) subject to disorder and frustrating interactions. This solvable model provides insight into the possibility of coexistence of super uidity and glassy density order, as well as into the nature of the coexistence phase (the superglass). In particular, for the considered mean field model I prove the existence of a superglass phase. This complements the numerical evidence for such phases provided by quantum Monte Carlo investigations in finite dimensions and on random graphs. Those were, however, limited to finite temperature, and could thus not fully elucidate the structure of the phases at T = 0. In contrast, my analytical approach allows one to understand the quantum phase transition between glassy superfluid and insulator, and the non-trivial role played by glassy correlations. When the frustrated interactions are strong enough, the superfluid order may be destroyed. As I will show in a mean field model, this happens within the glass phase of the system, where a disorder induced superfluid-insulator phase transition takes place to give way to a frustrated Bose glass. The glassy background on top of which this happens leads to many interesting phenomena which seem not to have been noticed before. To understand the nature of the glassy superfluid-insulator quantum phase transition at zero temperature and the transport properties on the insulating, Bose glass side of the transition is the goal of the third part of my thesis. To address the above questions, I studied an exactly solvable model of a glassy superfluid-insulator quantum phase transition on a Bethe lattice geometry with high connectivity. My main results can be summarized as follows: i) I found that the superfluid-insulator transition is shifted to stronger hopping. This is a result of the pseudo gap in the density of states of the glass state, which tends to strongly disfavor the onset of superfluidity. ii) In the glassy insulator, the discrete local energy levels become broadened due to the quantum fluctuations.The level-broadening process appears as a phase transition which has strong similarities with an Anderson localization transition, and has implications on many body localization. By using the locator expansion for bosons I found that, the glassy insulator has a finite mobility edge for the bosonic excitations, which, however, does not close upon approaching the SI quantum phase transition point. This finding helps to understand the nature of the superfluid-to-frustrated Bose glass transition: the superfluid emerges as a collective phase ordering phenomenon at zero temperature, and not as a condensation in to a single particle delocalized state, in contrast to opposite predictions in the recent literatures. The existence of a mobility edge in the insulator suggests the possibility of phononless, activated transport in the bosonic insulator, which might be a candidate explanation for the experimentally seen activated transport, which has remained a mystery for a long time.
We propose a quantum model consisting of an ensemble of overdamped spin−1/2 particles with ferromagnetic couplings, driven by a radially homogeneous magnetic field. The spontaneous magnetization of the spin components breaks the SO(3) (or 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.