Adiabatic Perturbation Theory: From Landau–Zener Problem to Quenching Through a Quantum Critical Point

Grandi, C. De; Polkovnikov, Anatoli

doi:10.1007/978-3-642-11470-0_4

Cited by 49 publications

(90 citation statements)

References 75 publications

(152 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This prediction was recently confirmed in cold-atom experiments with accelerated optical lattices (Zenesini, Lignier, Tayebirad et al, 2009). An analogous mechanism also explains the amount of energy injected into a system upon crossing a quantum-critical point or parameter changes in a gapless phase (Dziarmaga, 2010), as obtained from adiabatic perturbation theory (Grandi and Polkovnikov, 2010). In these cases the excitation energy typically behaves as ΔEðτÞ ∼ τ −η for large ramp times τ → ∞, with the positive exponent η depending on the details of the system and the ramp protocol.…”

Section: A Excitation Energy After a Continuous Parameter Changementioning

confidence: 93%

Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

View full text Add to dashboard Buy / Rent full text

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a selfconsistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

show abstract

Section: A Excitation Energy After a Continuous Parameter Changementioning

confidence: 93%

Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

View full text Add to dashboard Buy / Rent full text

show abstract

“…As shown in Refs. [26,37], this response is closely related to the geometrical properties of the ground state via 1 2 sin…”

Section: A Sweep Protocol and Dynamical Chern Numbermentioning

confidence: 99%

Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect

et al. 2017

View full text Add to dashboard Buy / Rent full text

We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H(sin theta cos phi, sin theta sin phi cos theta) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for alpha < 1. We report a divergence of the Berry curvature at alpha(c) = 1 for magnetic fields aligned along the equator theta = pi/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schrodinger approach we find that, for a fixed field sweep velocity theta(t) = vt, the bath induces a crossover from ( quasi) adiabatic to nonadiabatic dynamical behavior when the spin bath coupling a increases. We also investigate the particular regime H/omega(c) << v/H << 1 with large bath cutoff frequency.c, where the dynamical Chern number vanishes already at alpha = 1/2. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of alpha = 1/2. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium. Disciplines Condensed Matter Physics | Physics CommentsThis article is published as Henriet, Loïc, Antonio Sclocchi, Peter P. Orth, and Karyn Le Hur. "Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect." Physical Review B 95, no. 5 (2017) We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H (sin θ cos φ, sin θ sin φ, cos θ ) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for α < 1. We report a divergence of the Berry curvature at α c = 1 for magnetic fields aligned along the equator θ = π/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs a...

show abstract

“…The quantities considered so far could have in principle been obtained by using adiabatic perturbation theory [31], since our perturbative results capture only the lowest order correction in J z /J to the above physical quantities. Therefore, we now focus on the spin flip correlation function S + S − , which contains the bosonic fields in the exponent and demonstrates the non-perturbative nature of bosonization: the present approach yields to first correction in J z to the exponent of the spin-flip correlation function.…”

mentioning

confidence: 99%

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

2013

View full text Add to dashboard Buy / Rent full text

We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to swithcing on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a non-equilibrium situation.PACS numbers: 71.10. Pm,75.10.Jm,05.70.Ln, While it is difficult to study genuine non-equilibrium dynamics in solid state systems due to the presence of many relaxation channels (phonons, impurities, interactions etc.), cold atoms in optical lattices provide an ideal laboratory for non-equilibrium investigations due to the high degree of control over various dissipation mechanisms. Cold-atom experiments in the past decade have explored a wide variety of non-equilibrium quantum dynamics in previously inaccessible regimes [1,2]. This has also led to an increasing amount of theoretical activity [2,3]. Key issues include thermalization as well as equilibration and their relation to integrability [2], pumping beyond the adiabatic limit or quantum fluctuation relations [4], and universal near-adiabatic dynamics in quantum critical systems [2,3]. Linear quenches occuring over a finite time can interpolate between the more familiar limits of an instantaneous quench and an adiabatic sweep. Very recently, a few experiments have examined the response of many-body experiments to such finitetime quenches [5,6]. It is thus of vital current interest to address the dynamics under linear sweeps of system parameters such as interaction strength.The response of a system to an external perturbation depends sensitively on its spatial dimension, as famously demonstrated in the experiment of Ref. [7]. There, one dimensional interacting bosons did not reach thermalization within the experimental timescale, while their higher dimensional realizations did. One dimensional systems are notoriously strongly correlated due to the limited phase space for scattering. The non-interacting ground state is immediately destroyed by interactions, forming a Luttinger liquid (LL) in many instances [8,9], and described by critical phenomena of collective modes with anomalous (non-integer) power-law dependence of correlation functions.Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17]. For an abrupt interaction change, certain observables revealed universal LL ...

show abstract

Adiabatic Perturbation Theory: From Landau–Zener Problem to Quenching Through a Quantum Critical Point

Cited by 49 publications

References 75 publications

Nonequilibrium dynamical mean-field theory and its applications

Nonequilibrium dynamical mean-field theory and its applications

Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

Contact Info

Product

Resources

About