Measurement-induced quantum criticality under continuous monitoring

Fuji, Yohei; Ashida, Yuto

doi:10.1103/physrevb.102.054302

Cited by 140 publications

(57 citation statements)

References 75 publications

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“…27,28,29]. Also in this case entanglement phase transitions have been identified [22,30]. A crucial feature of these transitions is that they are invisible to the average dynamics but only appears at the level of single quantum many-body states.…”

Section: Introductionmentioning

confidence: 85%

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: 85%

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 turn, if the unitary evolution is implemented by a time-independent Hamiltonian, the origin of the phase transition in terms of non-commuting operators becomes directly apparent [35][36][37][38][39][40][41]. Repeatedly measuring a set of local operators {O l } then projects the system towards a shared eigenstate of all the operators O l .…”

Section: Perspectives On Measurement-induced Dynamics: a Recapmentioning

confidence: 99%

“…The Hamiltonian, however, for [H, O l ] = 0 is not compatible with the measurements, and constantly pushes the system out of the eigenstate manifold. The wave function then displays a volume law (logarithmically growing) entanglement entropy if the evolution is dominated by a generic (integrable) Hamiltonian, and an area law if instead the measurement-induced collapse into eigenstates dominates [35][36][37][38][39][40][41]. While this competition between non-commuting operators is reminiscent of a quantum phase transition in the ground state of a Hamiltonian, it also reveals a crucial difference; when measuring L different operators O l , and each operator has a number of n O different eigenstates, then, due to the probabilistic nature of the measurement process, the steady state will experience a macroscopic degeneracy of O(n L O ) compatible wave functions.…”

Section: Perspectives On Measurement-induced Dynamics: a Recapmentioning

confidence: 99%

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Continuous gaussian measurements of the free boson CFT: A model for exactly solvable and detectable measurement-induced dynamics

2022

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Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance. Defying the complications imposed by the non-linear and stochastic nature of the measurement process, we introduce a scenario of measurement-induced many body evolution, which possesses an exact analytical solution: bosonic Gaussian measurements. The evolution features a competition between the continuous observation of linear boson operators and a free Hamiltonian, and it is characterized by a unique and exactly solvable covariance matrix. Within this framework, we then consider an elementary model for quantum criticality, the free boson conformal field theory, and investigate in which way criticality is modified under measurements. Depending on the measurement protocol, we distinguish three fundamental scenarios (a) enriched quantum criticality, characterized by a logarithmic entanglement growth with a floating prefactor, or the loss of criticality, indicated by an entanglement growth with either (b) an area-law or (c) a volume-law. For each scenario, we discuss the impact of imperfect measurements, which reduce the purity of the wavefunction and are equivalent to Markovian decoherence, and present a set of observables, e.g., real-space correlations, the relaxation time, and the entanglement structure, to classify the measurement-induced dynamics for both pure and mixed states. Finally, we present an experimental tomography scheme, which grants access to the density operator of the system by using the continuous measurement record only.

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Measurement-induced quantum criticality under continuous monitoring

Cited by 140 publications

References 75 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

Continuous gaussian measurements of the free boson CFT: A model for exactly solvable and detectable measurement-induced dynamics

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