Measurement-induced topological entanglement transitions in symmetric random quantum circuits

Lavasani, Ali; Alavirad, Yahya; Barkeshli, Maissam

doi:10.1038/s41567-020-01112-z

Cited by 217 publications

(147 citation statements)

References 28 publications

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“…We leave it to future work to study this finding in more detail, e.g., by looking at other indicators such as the topological entanglement entropy or the appropriate string order parameter [70].…”

Section: E Signatures Of Spt Ordermentioning

confidence: 98%

Quantum scars and bulk coherence in a symmetry-protected topological phase

2021

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Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence of weakly entangled states. At the same time, coherence of edge modes in certain symmetry-protected topological (SPT) phases can persist away from the ground state. In this work we show the existence of many-body scars and their implications on bulk coherence in such an SPT phase. To this end, we study the eigenstate properties and the dynamics of an interacting spin-1/2 chain with three-site "cluster" terms hosting a Z 2 × Z 2 SPT phase. Focusing on the weakly interacting regime, we find that eigenstates with volume-law entanglement coexist with area-law entangled eigenstates throughout the spectrum. We show that a subset of the latter can be constructed by virtue of repeated cluster excitations on the even or odd sublattice of the chain, resulting in an equidistant "tower" of states, analogous to the phenomenology of quantum many-body scars. We further demonstrate that these scarred eigenstates support nonthermal expectation values of local cluster operators in the bulk and exhibit signatures of topological order even at finite energy densities. Studying the dynamics for out-of-equilibrium states drawn from the noninteracting "cluster basis," we unveil that nonthermalizing bulk dynamics can be observed on long timescales if clusters on odd and even sites are energetically detuned. In this case, cluster excitations remain essentially confined to one of the two sublattices such that inhomogeneous cluster configurations cannot equilibrate and thermalization of the full system is impeded. Our work sheds light on the role of quantum many-body scars in preserving SPT order at finite temperature and the possibility of coherent bulk dynamics in models with SPT order beyond the existence of long-lived edge modes.

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Section: E Signatures Of Spt Ordermentioning

confidence: 98%

Quantum scars and bulk coherence in a symmetry-protected topological phase

2021

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“…It was further demonstrated in Ref. [27][28][29] that repeatedly measuring local terms of the many-body Hamiltonian during the quantum dynamics can stabilize different quantum phases in the final steady state. One can even drive quantum phase transitions by varying the measurement strength of different Hamiltonian terms.…”

Section: Introductionmentioning

confidence: 98%

Decoherent quench dynamics across quantum phase transitions

et al. 2021

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We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})}t-∼τ2νz/(1+2νz) for when the system falls out of equilibrium and the associated freeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})}ξ‾∼τν/(1+2νz) show power-law scaling with respect to the quench rate 1/\tau1/τ, where the exponents depend on the correlation length exponent \nuν and the dynamical exponent zz associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.

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“…This transition has been observed in various settings including random Haar circuits, random Clifford circuits, Floquet quantum circuits, etc., [6][7][8][9][10][11][12][13][14]. It is continuous and enjoys an emergent conformal symmetry at the critical point.…”

mentioning

confidence: 99%

“…[57] Without the coupling between the left and the right chains, μ ¼ 0, the action is invariant under two Oð2Þ × Oð2Þ for the left and the right chains, respectively, [58] In this case we have δG 12 RR ¼ δG [55]. So we omit the subscript of the left and right chains.…”

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confidence: 99%

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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Measurement-induced topological entanglement transitions in symmetric random quantum circuits

Cited by 217 publications

References 28 publications

Quantum scars and bulk coherence in a symmetry-protected topological phase

Quantum scars and bulk coherence in a symmetry-protected topological phase

Decoherent quench dynamics across quantum phase transitions

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

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