17 research outputs found
Universal nonequilibrium quantum dynamics in imaginary time
We propose a method to study dynamical response of a quantum system by
evolving it with an imaginary-time dependent Hamiltonian. The leading
non-adiabatic response of the system driven to a quantum-critical point is
universal and characterized by the same exponents in real and imaginary time.
For a linear quench protocol, the fidelity susceptibility and the geometric
tensor naturally emerge in the response functions. Beyond linear response, we
extend the finite-size scaling theory of quantum phase transitions to
non-equilibrium setups. This allows, e.g., for studies of quantum phase
transitions in systems of fixed finite size by monitoring expectation values as
a function of the quench velocity. Non-equilibrium imaginary-time dynamics is
also amenable to quantum Monte Carlo (QMC) simulations, with a scheme that we
introduce here and apply to quenches of the transverse-field Ising model to
quantum-critical points in one and two dimensions. The QMC method is generic
and can be applied to a wide range of models and non-equilibrium setups.Comment: 8 pages, 3 figures. Expanded, final published versio
Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy
We study the excitation energy for slow changes of the hopping parameter in
the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The
excitation energy vanishes algebraically for long ramp times with an exponent
that depends on whether the ramp takes place within the metallic phase, within
the insulating phase, or across the Mott transition line. For ramps within
metallic or insulating phase the exponents are in agreement with a perturbative
analysis for small ramps. The perturbative expression quite generally shows
that the exponent depends explicitly on the spectrum of the system in the
initial state and on the smoothness of the ramp protocol. This explains the
qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g.,
Mott insulating) systems. For gapped systems the asymptotic behavior of the
excitation energy depends only on the ramp protocol and its decay becomes
faster for smoother ramps. For gapless systems and sufficiently smooth ramps
the asymptotics are ramp-independent and depend only on the intrinsic spectrum
of the system. However, the intrinsic behavior is unobservable if the ramp is
not smooth enough. This is relevant for ramps to small interaction in the
fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation
energy cannot be observed for a linear ramp due to its kinks at the beginning
and the end.Comment: 24 pages, 6 figure
Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
We discuss the application of the adiabatic perturbation theory to analyze
the dynamics in various systems in the limit of slow parametric changes of the
Hamiltonian. We first consider a two-level system and give an elementary
derivation of the asymptotics of the transition probability when the tuning
parameter slowly changes in the finite range. Then we apply this perturbation
theory to many-particle systems with low energy spectrum characterized by
quasiparticle excitations. Within this approach we derive the scaling of
various quantities such as the density of generated defects, entropy and
energy. We discuss the applications of this approach to a specific situation
where the system crosses a quantum critical point. We also show the connection
between adiabatic and sudden quenches near a quantum phase transitions and
discuss the effects of quasiparticle statistics on slow and sudden quenches at
finite temperatures.Comment: 20 pages, 3 figures, contribution to "Quantum Quenching, Annealing
and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes
in Phys., Springer, Heidelberg (2009, to be published), reference correcte
Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
We review recent theoretical work on two closely related issues: excitation
of an isolated quantum condensed matter system driven adiabatically across a
continuous quantum phase transition or a gapless phase, and apparent relaxation
of an excited system after a sudden quench of a parameter in its Hamiltonian.
Accordingly the review is divided into two parts. The first part revolves
around a quantum version of the Kibble-Zurek mechanism including also phenomena
that go beyond this simple paradigm. What they have in common is that
excitation of a gapless many-body system scales with a power of the driving
rate. The second part attempts a systematic presentation of recent results and
conjectures on apparent relaxation of a pure state of an isolated quantum
many-body system after its excitation by a sudden quench. This research is
motivated in part by recent experimental developments in the physics of
ultracold atoms with potential applications in the adiabatic quantum state
preparation and quantum computation.Comment: 117 pages; review accepted in Advances in Physic
Quench dynamics near a quantum critical point
We study the dynamical response of a system to a sudden change of the tuning parameter λ starting (or ending) at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order m at the quantum critical point, where m is related to the power of the quench. Precisely for sudden quenches, the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite-temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold-atom experiments