Researchers have discovered that a specific type of many-body system exhibits behavior akin to flocking when monitored, a surprising result given such systems typically produce only weak quantum signatures in stable states. Jacob F. Steiner, Felix von Oppen, and Reinhold Egger report finding power-law quantum correlations between spin density and charge current for weak monitoring strengths and ferromagnetic spin interactions, identifying this as a hallmark of the phenomenon. The work demonstrates that monitoring strength has a dual role, generating these quantum correlations when weak but driving a Berezinskii-Kosterlitz-Thouless phase transition to a short-range correlated state at larger strengths.

Weak Monitoring Generates Quantum Correlations in Spinful Luttinger Liquids

A specific type of quantum system, the spinful Luttinger liquid, demonstrates behavior reminiscent of flocking birds when subjected to observation, even though traditionally such systems yield only faint quantum signals in stable conditions. This emergence of active matter-like behavior from a pure quantum state is unexpected, as conventional active matter typically requires complex, mixed states to exhibit similar collective motion. The work details how the strength of this observation, or “monitoring,” fundamentally alters the system’s quantum properties, creating and then destroying long-range correlations.

The team designed the monitoring process to induce directed movement, effectively providing the system with the defining characteristic of quantum active matter, self-propulsion. Calculations reveal that the resulting steady-state correlations between spin density and charge current exhibit power-law behavior at long distances, signifying a quasi-long-range order within the ensemble.

Beyond a certain strength, the same observation that initially generated these active quantum correlations drives a Berezinskii-Kosterlitz-Thouless (BKT) phase transition, collapsing the long-range order into a state with only short-range correlations. This transition is linked to charge sharpening transitions observed in monitored quantum systems with U(1) symmetry. This theoretical framework builds upon recent investigations of spinless models undergoing monitoring with hermitian operators, providing a more comprehensive understanding of the underlying physics.

Lattice models of similar U(1)-symmetric monitored systems also exhibit a transition between phases with differing entanglement properties, further reinforcing the importance of monitoring in controlling quantum correlations. The team’s analysis of measurement-averaged equal-time connected correlation functions revealed exponential decay in the short-range phase, with a length scale determined by the monitoring strength. The coefficient governing this behavior increases with the level of activity driven by the measurements, demonstrating a direct link between observation and the strength of quantum correlations.

When the monitoring strength exceeds a critical threshold, the pure-state dynamics transition to a phase characterized by exponentially decaying correlations, signifying a loss of long-range order. The team’s model, a one-dimensional chain of spin-fermions with ferromagnetic Ising coupling, poses the question of whether directed particle motion and alignment do not necessarily require incoherent, classical processes. The resulting algebraic phase, characterized by these long-range correlations, is strongly quantum in nature, and cannot be created using simple, shallow quantum circuits.

Conversely, the short-range correlated phase emerges from the quantum Zeno effect, where frequent measurements effectively freeze the system’s evolution. The work demonstrates that quantum active matter can be realized in monitored interacting fermion chains, where monitoring induces self-propulsion but ultimately leads to a BKT transition between phases with differing levels of quantum active correlations. This transition highlights the delicate balance between observation and the preservation of quantum coherence in many-body systems, offering new insights into the fundamental interplay between measurement and quantum dynamics.

Monitored Dynamics Mimic Active Matter via Pure-State Evolution

Unlike conventional active matter systems reliant on mixed quantum states, this behavior arises within the confines of pure-state dynamics driven by continuous quantum measurements; this distinction is critical because it establishes quantumness as a fundamental requirement for this type of activity. This approach diverges significantly from previous studies of active matter, which often rely on ensemble-averaged states and Lindblad evolution, and instead focuses on the evolution of individual pure quantum states conditioned on measurement outcomes. This preservation is achieved through the stochastic Schrödinger equation, which governs the monitored evolution of the system and ensures normalization of the quantum state given a pure initial condition.

The resulting dynamics reveal that signatures of quantum active motion persist at long times, a finding that challenges the expectation of transient correlations in weakly monitored systems. The strength of the monitoring plays a dual role in shaping the system’s behavior; initially, increasing monitoring strength or ferromagnetic coupling causes these quantum correlations to grow. This suggests a level of quantum entanglement beyond what is achievable with simple classical simulations, reinforcing the idea that this is a genuinely quantum form of active matter.

Cartoon depictions within the study illustrate how spin-independent hopping allows for bidirectional motion, while monitoring introduces a unidirectional component, driving the self-propulsion essential for active matter behavior. The implications of this work extend beyond the specific model studied.

Ferromagnetic Interactions and Monitoring Drive Incipient Quantum Flocking

The work demonstrates that signatures of active matter can arise even in ensembles of pure states undergoing monitored quantum dynamics, challenging the expectation that active matter necessitates complex, mixed states. Initial increases in monitoring strength or ferromagnetic coupling lead to growth in these correlations, effectively forming an incipient quantum flock.

The study employed a 1D quantum active model of spin-fermions with ferromagnetic Ising coupling, utilizing only monitored quantum dynamics, unitary dynamics combined with weak continuous measurements. Calculations indicate an entanglement transition, suggesting a boundary between volume-law entangled phases and a potential demarcation between quantum and classical active phases.

The Ising interaction enhances spin current correlations while reducing spin density correlations, a result the researchers rationalize by noting that Ising interactions favor alignment of adjacent spins and thus promote quantum flocking. In the strong-coupling phase, with large interactions, the nonlinearity leads to a Gaussian fixed point with a mass term in the boson dispersion, resulting in exponential decay and only short-range correlations.

Berezinskii-Kosterlitz-Thouless Transition Modifies Active Quantum Correlations

These correlations emerge when monitoring strength is weak and spin interactions are ferromagnetic, a surprising result given that traditional active matter relies on complex, mixed quantum states. The work demonstrates that such behavior can originate solely from unitary time evolution and quantum measurements, challenging conventional expectations for systems exhibiting self-propelled dynamics. Researchers utilized renormalization group equations to map the phase diagram, indicating an entanglement transition and a boundary separating a quasi-long-range quantum active phase from the short-range correlated phase.

Analysis of the system’s effective Hamiltonian revealed that monitoring introduces a coupling that influences both parity-odd spin-charge interactions, giving rise to the active correlations, and a parity-even nonlinearity that drives the transition. “Monitoring plays a dual role,” in both generating the active correlations and inducing the phase transition, highlighting the complex interplay between observation and system dynamics.

Calculations indicate exponential decay of correlations with a characteristic length scale in the short-range phase. While a detailed study of this subsequent entanglement transition remains for future work, the current findings establish a clear connection between monitoring, phase transitions, and the emergence of active quantum matter. The researchers note that the observed transition occurs in a two-dimensional quantum system, differing from the classical case observed in two spatial dimensions.

The algebraic phase, possessing strong quantum characteristics, cannot be created using simple, shallow quantum circuits, indicating a high degree of entanglement. This interplay between monitoring strength and resulting correlations offers a new perspective on the control and manipulation of quantum many-body systems.

The team’s analysis indicates that the system’s evolution toward a dark state does not involve a jump term, describing a pure-state evolution governed by nonhermitian dynamics. Further investigation using matrix product state methods may prove useful in characterizing the entanglement transition to the weakly quantum area-law entangled phase, a topic left for future research due to current limitations in the bosonization approach.

👉 More information
🗞 Active Quantum Matter from Monitored Pure-State Dynamics
✍️ Jacob F. Steiner, Felix von Oppen and Reinhold Egger
🧠 DOI: http://link.aps.org/doi/10.1103/zhdk-kgzx

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