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arXiv:2406.00521 · Scientific Reports

Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry

C Manju, Arul Lakshminarayan, Uma Divakaran

Published Oct 7, 2025• 3 citations
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Abstract

The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. This work finds a continuous phase transition when disorder breaks permutation symmetry, with details of the transition being controlled by the degree of chaos in the clean limit. The system changes from an area law entangled phase in the permutation symmetric subspace where collective variables exist to volume law entanglement in the full Hilbert space, beyond a critical strength of the disorder. This has potential implications for general many body physics, as well as technologies such as transmon qubits.

DOI
10.1038/s41598-025-18895-x

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The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. This work finds a continuous phase transition when disorder breaks permutation symmetry, with details of the transition being controlled by the degree of chaos in the clean limit. The system changes from an area law entangled phase in the permutation symmetric subspace where collective variables exist to volume law entanglement in the full Hilbert space, beyond a critical strength of the disorder. This has potential implications for general many body physics, as well as technologies such as transmon qubits.
This study explores the effects of introducing a symmetry-breaking disorder on the dynamics of a system invariant under particle permutation. The disorder forces quantum states, confined to the N+1-dimensional completely symmetric space to penetrate the exponentially large 2^{N}-dimensional Hilbert space of N particles. In particular, we focus on the quantum kicked top as a Floquet system of N qubits and use linear entropy, measuring single-qubit entanglement, to investigate the changes in the timescales and values of saturation when disorder is introduced. In the near-integrable regime of the kicked top, we study the robustness of quantum revivals to disorder. We also find that a classical calculation yields the quantum single-qubit entanglement to remarkable accuracy in the disorder-free limit. The disorder, on the other hand, is modeled in the form of noise, which again fits well with the numerical calculations. We measure the extent to which the dynamics is retained within the symmetric subspace and its spreading to the full Hilbert space using different quantities. We show that increasing disorder drives the system to a chaotic phase in full Hilbert space, as also supported by the spectral statistics. We find that there is robustness to disorder in the system, and this is a function of how chaotic the kicked top is.
We investigate disordered one- and two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin- and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.
Local measurements in quantum systems are projective operations which act to counteract the spread of quantum entanglement. Recent work has shown that local, random measurements applied to a generic volume-law entanglement generating many-body system are able to force a transition into an area-law phase. This work shows that projective operations can also force a similar classical phase transition; we show that local projections in a chaotic system can freeze information dynamics. In rough analogy with measurement-induced phase transitions, this is characterized by an absence of information spreading instead of entanglement entropy. We leverage a damage-spreading model of the classical transition to predict the butterfly velocity of the system both near to and away from the transition point. We map out the full phase diagram and show that the critical point is shifted by local projections, but remains in the directed percolation universality class. We discuss the implication for other classical chaotic many-body systems and the relation to synchronization transitions.
We investigate disordered oneand two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the basis dependence of state delocalization indicators such as the number of principal components is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spinand fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.
Abstract Non-equilibrium phase transitions are a vibrant frontier in physics, driving breakthroughs across diverse disciplines in recent years. Thermal spin ensembles, a captivating many-body quantum system, have harnessed their collective strengths to set remarkable measurement benchmarks in equilibrium. However, their non-equilibrium dynamics remain unexplored, with nonlinear interactions among constituents offering a rich playground for phase transition studies. Here, we employ nonlinear magnetic feedback to achieve real-time observation and control of phase transitions in a driven-dissipative spin ensemble, unveiling dynamic shifts between limit cycles, subharmonics, and chaos. This work not only deepens our grasp of critical phenomena in non-equilibrium systems but also paves the way for chaos-based sensing and information processing technologies, bridging fundamental physics with transformative applications.
The authors investigate here the dynamics of free fermions in a random potential system under continuous monitoring. Repeated measurements are known to induce an entanglement phase transition from a logarithmically entangled critical state to area law, while disorder leads to Anderson localization. They show that their interplay results in a stable critical phase at finite disorder strength and dissipation, which drive a transition consistent with Berezinskii-Kosterlitz-Thouless universality. This work is important for testing such phase transitions in quantum dot arrays and nanowires.