Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law

Alberton, Ori; Buchhold, Michael; Diehl, Sebastian

doi:10.1103/physrevlett.126.170602

Cited by 216 publications

(169 citation statements)

References 49 publications

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“…We stress that the many-body nature of the problem is encoded in the competition between unitary entangling dynamics and local measurements, rather than in the unmeasured system itself (the quantum Ising chain) which is integrable through free fermions techniques. We also note that to the best of our knowledge this map-ping cannot be used to exactly solve the problem for the measurement protocol considered in this work, corresponding to a Born rule [40], as opposed to other stochastic settings [41,42] which also show genuine many-body signatures such as entanglement phase transitions.…”

Section: Introductionmentioning

confidence: 99%

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Biella

Schiró

2021

Quantum

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It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

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Section: Introductionmentioning

confidence: 99%

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Biella

Schiró

2021

Quantum

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“…These measurement-induced transitions occur in a wide variety of models, including random circuits , Hamiltonian systems [36][37][38][39][40][41][42][43][44], and measurement-only models [28,45,46,57], and they exhibit universal behavior. However, the determination of the relevant universality classes has proved to be a subtle issue.…”

Section: Introductionmentioning

confidence: 99%

Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits

2021

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Entanglement transitions in quantum dynamics present a novel class of phase transitions in nonequilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with monitored random measurements, the steady state can exhibit a phase transition between volume-and area-law entanglement. There is a correspondence between measurement-induced transitions in nonunitary quantum circuits in d spatial dimensions and classical statistical mechanical models in d + 1 dimensions. In certain limits these models map to percolation, but there is analytical and numerical evidence to suggest that away from these limits the universality class should generically be distinct from percolation. Intriguingly, despite these arguments, numerics on 1 + 1D qubit circuits give bulk exponents which are nonetheless close to those of 2D percolation, with some possible differences in surface behavior. In the first part of this work we explore the critical properties of 2 + 1D Clifford circuits. In the bulk, we find many properties suggested by the percolation picture, including several matching bulk exponents, and an inverse power law for the critical entanglement growth, S(t, L) ∼ L(1 − a/t ), which saturates to an area law. We then utilize a graph-state-based algorithm to analyze in 1 + 1D and 2 + 1D the critical properties of entanglement clusters in the steady state. We show that in a model with a simple geometric map to percolation-the projective transverse field Ising model-these entanglement clusters are governed by percolation surface exponents. However, in the Clifford models we find large deviations in the cluster exponents from those of surface percolation, highlighting the breakdown of any possible geometric map to percolation. Given the evidence for deviations from the percolation universality class, our results raise the question of why nonetheless many bulk properties behave similarly to those of percolation.

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“…In addition to measurement-induced phase transitions in random hybrid circuits, an interesting distinct class of phenomena arise in noninteracting fermion circuits, which can host a critical phase when subjected to weak measurements. In this situation, the entanglement entropy shows a log scaling with subsystem size in an entire phase instead of just at the transition point [24][25][26][27][28][29]. As the measurement strength is further increased, a phase transition from the critical phase to the area-law phase occurs [25,29].…”

mentioning

confidence: 99%

“…In this situation, the entanglement entropy shows a log scaling with subsystem size in an entire phase instead of just at the transition point [24][25][26][27][28][29]. As the measurement strength is further increased, a phase transition from the critical phase to the area-law phase occurs [25,29].…”

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confidence: 99%

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Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model

et al. 2021

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We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-N limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK 2 chains, the model features a continuous Oð2Þ symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous Oð2Þ symmetry is explicitly lowered to a discrete C 4 symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by C 4 symmetry breaking. We also verify the large-N critical exponents by numerically solving the Schwinger-Dyson equation.

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Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law

Cited by 216 publications

References 49 publications

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits

Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model

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