Geometric Phase Contribution to Quantum Nonequilibrium Many-Body Dynamics

Tomka, Michael; Polkovnikov, Anatoli; Gritsev, Vladimir

doi:10.1103/physrevlett.108.080404

Cited by 24 publications

(19 citation statements)

References 18 publications

(24 reference statements)

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“…Recently, multispin interactions were demonstrated to arise in Floquet driven lattices [42,43]. We finally observe that the multicritical points in the generalized cluster-Ising models can be used to investigate nonequilibrium dynamics in manybody physics [44,45]. It is interesting to study the nonadiabatic driving scheme across the multicritical points in cluster-Ising spin chain and the interplay between geometric phase and dynamics in the near future.…”

Section: Interactionmentioning

confidence: 79%

Scaling of geometric phase versus band structure in cluster-Ising models

et al. 2017

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We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z=1 or z=2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.

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Section: Interactionmentioning

confidence: 79%

Scaling of geometric phase versus band structure in cluster-Ising models

et al. 2017

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“…We allow M to vary periodically with time so that M (t + T ) = M (t). Equation (14) implies that the Heisenberg equations for the operators b n (t) are given by…”

Section: Floquet Time Evolution and End Modesmentioning

confidence: 99%

Generating end modes in a superconducting wire by periodic driving of the hopping

2017

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We show that harmonic driving of either the magnitude or the phase of the nearest-neighbor hopping amplitude in a p-wave superconducting wire can generate modes localized near the ends of the wire. The Floquet eigenvalues of these modes can either be equal to ±1 (which is known to occur in other models) or can lie near other values in complex conjugate pairs which is unusual; we call the latter anomalous end modes. All the end modes have equal probabilities of particles and holes. If the amplitude of driving is small, we observe an interesting bulk-boundary correspondence for the anomalous end modes: the Floquet eigenvalues and the peaks of the Fourier transform of these end modes lie close to the Floquet eigenvalues and momenta at which the Floquet eigenvalues of the bulk system have extrema.

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“…Otherwise contributions from short wavelength modes become dominant and hence the low-energy singularities associated with the critical point become subleading [419,515]. Very recently, a study of the influence of the geometric phase on the non-equilibrium dynamics of a quantum many-body system has been reported [544]; it has been shown that for fast driving the GP strongly affects transitions between levels, and the possibility of the emergence of a dynamical transition due to a competition between the geometrical and dynamical phases has been pointed out.…”

Section: (C) Adiabatic Perturbation Theory: Slow and Sudden Quenchesmentioning

confidence: 99%

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

Dutta¹,

Aeppli²,

Chakrabarti³

et al. 2010

Preprint

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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Geometric Phase Contribution to Quantum Nonequilibrium Many-Body Dynamics

Cited by 24 publications

References 18 publications

Scaling of geometric phase versus band structure in cluster-Ising models

Scaling of geometric phase versus band structure in cluster-Ising models

Generating end modes in a superconducting wire by periodic driving of the hopping

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

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