Scaling of decoherence and energy flow in interacting quantum spin systems

Rossini, Davide; Vicari, Ettore

doi:10.1103/physreva.99.052113

Cited by 21 publications

(26 citation statements)

References 74 publications

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“…On the other hand, dissipation can be also exploited to engineer desired quantum states 7 , to perform quantum computation 8 , or even to prepare topological states of matter 9 . The possibility of analyzing the interplay between dissipation and quantum criticality [10][11][12][13][14][15] is also particularly intriguing. However, unfortunately, modeling the system-environment interaction within an analytic or numerical framework is in general a daunting task.…”

Section: Introductionmentioning

confidence: 99%

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Alba,

Carollo

2021

Preprint

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We investigate the interplay between unitary dynamics after a quantum quench and localized dissipation in a noninteracting fermionic chain. In particular, we consider the effect of gain and loss processes, for which fermions are added and removed incoherently. We focus on the hydrodynamic limit of large distances from the source of dissipation and of long times, with their ratio being fixed. In this limit, the localized dissipation gives rise to an effective delta potential (dissipative impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic description in terms of the fermionic occupations in the initial state and the reflection and transmission amplitudes of the impurity. We derive this hydrodynamic framework from the ab initio calculation of the microscopic dynamics. This allows us to analytically characterize the effect of dissipation for several theoretically relevant initial states, such as a uniform Fermi sea, homogeneous product states, or the inhomogeneous state obtained by joining two Fermi seas. In this latter setting, when both gain and loss processes are present, we observe the emergence of exotic nonequilibrium steady states with stepwise uniform density profiles. In all instances, for strong dissipation the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect.

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Section: Introductionmentioning

confidence: 99%

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Alba,

Carollo

2021

Preprint

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“…Indeed we consider infinite-size systems, for which we derive scaling laws extending to the large-time limit of the evolution described by the Lindblad equation, thus valid for the corresponding stationary states. We mention that dynamic scaling behaviors have been also put forward, and numerically checked, for open critical systems when the environment is constituted by a single qubit homogeneously coupled to the whole manybody system [10].…”

Section: Introductionmentioning

confidence: 99%

Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

Rossini

Vicari

2019

Phys. Rev. B

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We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions, in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a onedimensional lattice fermion gas undergoing a quantum Ising transition, in the presence of dissipative mechanisms which include local pumping and decay of particles. arXiv:1907.02631v1 [cond-mat.stat-mech]

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“…To achieve a more quantitative understanding of the role of projective measurements in this context, it is worth focusing on the quantum critical region, where universality can be helpful to control the dynamics of the system. Indeed, the out-of-equilibrium critical dynamics at continuous quantum transitions develops homogeneous scaling laws [30][31][32][33][34][35][36][37][38][39][40][41], even in the presence of dissipation [42,43]. One could ask whether similar scaling arguments hold in the above context, as well.…”

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confidence: 97%

Measurement-induced dynamics of many-body systems at quantum criticality

Rossini

Vicari

2020

Phys. Rev. B

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We consider a dynamic protocol for quantum many-body systems, which enables to study the interplay between unitary Hamiltonian driving and random local projective measurements. While the unitary dynamics tends to increase entanglement, local measurements tend to disentangle, thus favoring decoherence. Close to a quantum transition where the system develops critical correlations with diverging length scales, the competition of the two drivings is analyzed within a dynamic scaling framework, allowing us to identify a regime (dynamic scaling limit) where the two mechanisms develop a nontrivial interplay. We perform a numerical analysis of this protocol in a measurementdriven Ising chain, which supports the scaling laws we put forward. The local measurement process generally tends to suppress quantum correlations, even in the dynamic scaling limit. The power law of the decay of the quantum correlations turns out to be enhanced at the quantum transition.

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Scaling of decoherence and energy flow in interacting quantum spin systems

Cited by 21 publications

References 74 publications

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

Measurement-induced dynamics of many-body systems at quantum criticality

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