A numerical study has found that an open quantum model can form dense, finite clusters while retaining quantum coherence. The authors describe the combined pattern as compelling numerical evidence for quantum motility-induced phase separation, or MIPS, in a one-dimensional open quantum system. The result is a model calculation, not a demonstration in a physical system.
MIPS is the study’s term for a separation pattern linked to active motion. The researchers asked whether a genuine quantum analogue exists and how quantum coherence relates to dissipative self-propulsion.
A simulated system kept out of equilibrium
The researchers modeled active hard-core bosons in one dimension. Their Lindblad model combines coherent quantum tunneling with dissipative jump processes. The system was initialized in a maximally mixed state with a fixed particle number, N = L/2.
They used exact-factorization Monte Carlo wave-function simulations, reporting numerically exact calculations for systems of up to L = 1000 lattice sites.
Finite clusters in the minimal model
The weak-amplitude minimal model was described as showing microphase separation, with dense clusters of finite characteristic size rather than one macroscopic domain. At g/ℏγ = 0.05, the reported scaling exponent for fluctuations in the number of particles within a subsystem was β ≈ 1.7. No confidence interval or formal uncertainty estimate was reported for that exponent.
The study reported genuine phase separation in the minimal model only in the singular limit where the quantum amplitude vanishes. At finite quantum amplitude, the reported behavior was instead characterized by clusters of finite size.
A possible phase-separation signal in a smaller test
The researchers also studied an extended model with nearest-neighbor repulsion. That version was reported to provide numerical evidence compatible with genuine phase separation and a divergent correlation length.
The extended-model result remains less settled because simulations without factorization reached only about L = 30 sites. The authors judged that size insufficient for reliable scaling of particle-number fluctuations. The thermodynamic-limit behavior remains unresolved.
Coherence survived inside the clusters
The clustered states did not lose all quantum coherence. In the minimal model, nearest-neighbor coherence C1 remained finite. At weak quantum amplitudes, coherence remained sizable out to about d = 7 lattice sites, while at strong amplitudes it decayed beyond d = 2. With positive nearest-neighbor repulsion, C1 was slightly suppressed, but coherence at larger distances was more robust.
The extended model also produced a signal indicative of spatial entanglement. At I/ℏγ = 2, negative partial-transpose eigenvalues were observed for g between 0.15 and 0.3, yielding nonzero negativity. At larger quantum amplitudes and distances, coherence had not converged for the reported trajectory count, so those values were treated as upper-bound estimates.
What the calculation does not establish
The authors interpret the numerical patterns as compelling evidence for quantum MIPS in the specified one-dimensional open quantum system, with clustered states retaining coherence. That interpretation does not establish quantum MIPS experimentally or show that the behavior extends beyond this model.
The study is an arXiv preprint, version 1, dated 26 August 2026. The authors state that data from all figures are available on Zenodo.
Paper data and sources
Original title: Quantum motility-induced phase separation
Authors: Laurin Brunner, Ricard Alert, Reyhaneh Khasseh, Markus Heyl
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text