Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

Divakaran, Uma; Dutta, Amit; Sen, Diptiman

doi:10.1103/physrevb.81.054306

Cited by 10 publications

(7 citation statements)

References 58 publications

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“…Refs. (Damski and Zurek, 2006;Divakaran et al, 2010) for particular cases). Likewise if there is a discontinuity in the second order derivative of g(t) asymptotically the transition probability in the LZ problem scales quadratically with acceleration.…”

Section: Slow Dynamics In Gapped and Gapless Systemsmentioning

confidence: 99%

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

et al. 2011

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This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. We discuss several aspects of the slow dynamics in driven systems and emphasize the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions. We also review recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis and discuss relaxation in integrable systems. Finally we overview key experiments probing quantum dynamics in cold atom systems and put them in the context of our current theoretical understanding.

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Section: Slow Dynamics In Gapped and Gapless Systemsmentioning

confidence: 99%

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

et al. 2011

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“…We now consider a similar problem where the parameter J − is varied linearly up to the critical point at which the variation is stopped for some time t w [555]. After this waiting time t w , the variation is once again resumed in the forward direction.…”

Section: (F) Generalized Quenching Schemesmentioning

confidence: 99%

Quantum phase transitions in transverse field spin models: from statistical physics to quantum information

Dutta¹,

Aeppli²,

Chakrabarti³

et al. 2010

Preprint

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112

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We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of some paradigmatic models, namely, the spin-1/2 Ising and XY models in a transverse field in one and higher spatial dimensions. Beginning with a brief overview of quantum phase transitions, we introduce the model Hamiltonians and discuss the equivalence between the quantum phase transition in such a model and the finite temperature phase transition in a higher dimensional classical model. We then provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies when possible. We also discuss Kitaev models, and some other exactly solvable spin systems in this context. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in details. We discuss novel phenomena like Griffiths-McCoy singularities associated with quantum phase transitions of lowdimensional transverse Ising models with random interactions and transverse fields. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models; we elaborate on the scaling behaviors of concurrence, entanglement entropy (for both pure and random models), quantum discord and quantum fidelity close to a quantum critical point. At the same time, we discuss the decoherence (or Loschmidt echo) of a qubit coupled to a quantum critical spin chain. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After briefly mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. We present a brief discussion on adiabatic perturbation theory indicating the limits of slow and sudden quenching; we introduce the concept of a generalized fidelity susceptibility in this context. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures (introduced in the previous section) is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing (or adiabatic quantum computation). The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.

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“…A study of the Landau-Zener problem with waiting at the minimum gap has been reported in Ref. [25]. It was observed that the waiting influences the excitation probability.…”

Section: Free Evolution and Decay Of Fidelitymentioning

confidence: 99%

Testing quantum adiabaticity with quench echo

Quan

Zurek²

2010

New J. Phys.

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Adiabaticity of quantum evolution is important in many settings; one example is the adiabatic quantum computation (AQC). Nevertheless, to date, there is no effective method available for testing the adiabaticity of the evolution for the case where the eigenenergies of the driven Hamiltonian are not known. We propose a simple method for checking adiabaticity of a quantum process for an arbitrary quantum system. We further propose an operational method for finding more efficient protocols that approximate adiabaticity, and suggest a "uniformly adiabatic" quench scheme based on the Kibble-Zurek mechanism for the case where the initial and the final Hamiltonians are given. This method should help in implementing AQC and other tasks where preserving the system in the ground state of a time-dependent Hamiltonian is desired.

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Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

Cited by 10 publications

References 58 publications

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Quantum phase transitions in transverse field spin models: from statistical physics to quantum information

Testing quantum adiabaticity with quench echo

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