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arXiv:2603.12629 · Physical Review Letters

Active quantum matter from monitored pure-state dynamics

Jacob F. Steiner, Felix von Oppen, Reinhold Egger

quant-phcond-mat.softcond-mat.stat-mechSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations• Revised Sep 15, 2026 (v2)
v1 · Mar 13, 2026v2 · Sep 15, 2026
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Abstract

Quantum many-body systems coupled to out-of-equilibrium reservoirs can behave as active matter and exhibit signs of flocking. However, the resulting steady states are highly mixed and carry only weak quantum signatures. We show that signatures of active matter also arise in ensembles of pure states undergoing monitored quantum dynamics. We consider a spinful Luttinger liquid subject to measurement processes that shuffle spin-up particles to the left and spin-down particles to the right. For weak monitoring strengths and ferromagnetic spin interactions, we find power-law quantum correlations between spin density and charge current, which we identify as a hallmark of active quantum matter. The monitoring plays a dual role, generating the quantum active correlations for weak strengths while driving a Berezinskii-Kosterlitz-Thouless (BKT) phase transition to a shortrange correlated state at larger strengths.

DOI
10.1103/zhdk-kgzx

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Quantum many-body systems coupled to out-of-equilibrium reservoirs can behave as active matter and exhibit signs of flocking. However, the resulting steady states are highly mixed and carry only weak quantum signatures. We show that signatures of active matter also arise in ensembles of pure states undergoing monitored quantum dynamics. We consider a spinful Luttinger liquid subject to measurement processes that shuffle spin-up particles to the left and spin-down particles to the right. For weak monitoring strengths and ferromagnetic spin interactions, we find power-law quantum correlations between spin density and charge current, which we identify as a hallmark of active quantum matter. The monitoring plays a dual role, generating the quantum active correlations for weak strengths while driving a Berezinskii-Kosterlitz-Thouless (BKT) phase transition to a shortrange correlated state at larger strengths.
We analytically study interacting Dirac fermions, described by the Thirring model, under weak local particle number measurements with monitoring rate $\ensuremath{\gamma}$. This system maps to a bosonic replica field theory, analyzed via the renormalization group. For a nonzero attractive interaction, a phase transition occurs at a critical measurement strength ${\ensuremath{\gamma}}_{c}$. When $\ensuremath{\gamma}>{\ensuremath{\gamma}}_{c}$, the system enters a localized phase characterized by exponentially decaying density-density correlations beyond a finite correlation length; for $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{c}$, the correlations decay algebraically. The transition is of Berezinskii-Kosterlitz-Thouless (BKT) type, reflected by a characteristic scaling of the correlation length. In the noninteracting limit, ${\ensuremath{\gamma}}_{c}\ensuremath{\rightarrow}0$ shifts to zero, reducing the algebraic phase to a single point in parameter space. This identifies weak measurements in the free case as an implicit double fine tuning to the critical end point of the BKT phase transition. Along the noninteracting line, we compute the entanglement entropy from density-density correlation functions and find no entanglement transition at nonzero measurement strength in the thermodynamic limit.
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 analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.
We study a dimerized spin chain with biaxial magnetic interacting ions in the presence of externally induced three-site interactions out of equilibrium. In the general case, the three-site interactions play a role in renormalizing the effective uniform magnetic field. We find that the existence of zero-energy Majorana modes is intricately related to the sign of Pfaffian of the Bogoliubov--de Gennes Hamiltonian and the relevant Z2{Z}_{2}Z2​ topological invariant. In contrast, we show that an exotic spin-liquid phase can emerge in the compass limit through a Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition. Such a BKT transition is characterized by a large dynamic exponent z=4z=4z=4, and the spin-liquid phase is robust under a uniform magnetic field. We find the relative entropy and the quantum discord can signal the BKT transitions. We also uncover a few differences in deriving the correlation functions for the systems with broken reflection symmetry.
We propose and analyze a new method for quantum metrology based on stable non-equilibrium states of quantum matter. Our approach utilizes quantum correlations stabilized by strong interactions and periodic driving. As an example, we present an explicit protocol to perform Floquet enhanced measurements of an oscillating magnetic field in Ising-interacting spin systems. Our protocol allows one to circumvent the interaction-induced decoherence associated with high density spin ensembles and is robust to the presence of noise and imperfections. Applications to nanoscale magnetic sensing and precision measurements are discussed.
Interspersing unitary dynamics with local measurements results in measurement-induced phases and transitions in many-body quantum systems. When the evolution is driven by a local Hamiltonian, two types of transitions have been observed, characterized by an abrupt change in the system size scaling of entanglement entropy. The critical point separates the strongly monitored area-law phase from a volume law or a subextensive, typically logarithmiclike, one at low measurement rates. Identifying the key ingredients responsible for the entanglement scaling in the weakly monitored phase is the key purpose of this work. For this purpose, we consider prototypical one-dimensional spin chains with local monitoring featuring the presence/absence of U(1) symmetry, integrability, and interactions. Using exact numerical methods, the system sizes studied reveal that the presence of interaction is always correlated to a volume law weakly monitored phase. In contrast, noninteracting systems present subextensive scaling of entanglement. Other characteristics, namely integrability or U(1) symmetry, do not play a role in the character of the entanglement phase.