First numerical evidence for quantum motility-induced phase separation… where activity and quantum coherence coexist

Abstract

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