63 research outputs found
Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
We investigate the non-equilibrium dynamics of the transverse field quantum
Ising chain evolving from an inhomogeneous initial state given by joining two
macroscopically different semi-infinite chains. We obtain integral expressions
for all two-point correlation functions of the Jordan-Wigner Majorana fermions
at any time and for any value of the transverse field. Using this result, we
compute analytically the profiles of various physical observables in the
space-time scaling limit and show that they can be obtained from a hydrodynamic
picture based on ballistically propagating quasiparticles. Going beyond the
hydrodynamic limit, we analyze the approach to the non-equilibrium steady state
and find that the leading late time corrections display a lattice effect. We
also study the fine structure of the propagating fronts which are found to be
described by the Airy kernel and its derivatives. Near the front we observe the
phenomenon of energy back-flow where the energy locally flows from the colder
to the hotter region
Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an symmetry
A spectrum exhibiting symmetry is expected to arise when a small
longitudinal field is introduced in the transverse-field Ising chain at its
quantum critical point. Evidence for this spectrum has recently come from
neutron scattering measurements in cobalt niobate, a quasi one-dimensional
Ising ferromagnet. Unlike its zero-temperature counterpart, the
finite-temperature dynamics of the model has not yet been determined. We study
the dynamical spin structure factor of the model at low frequencies and nonzero
temperatures, using the form factor method. Its frequency dependence is
singular, but differs from the diffusion form. The temperature dependence of
the nuclear magnetic resonance (NMR) relaxation rate has an activated form,
whose prefactor we also determine. We propose NMR experiments as a means to
further test the applicability of the description for CoNbO.Comment: 5 pages 2 figures - Supplementary Material 11 page
Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
The semiclassical approach introduced by Sachdev and collaborators proved to
be extremely successful in the study of quantum quenches in massive field
theories, both in homogeneous and inhomogeneous settings. While conceptually
very simple, this method allows one to obtain analytic predictions for several
observables when the density of excitations produced by the quench is small. At
the same time, a novel generalized hydrodynamic (GHD) approach, which captures
exactly many asymptotic features of the integrable dynamics, has recently been
introduced. Interestingly, also this theory has a natural interpretation in
terms of semiclassical particles and it is then natural to compare the two
approaches. This is the objective of this work: we carry out a systematic
comparison between the two methods in the prototypical example of the
sine-Gordon field theory. In particular, we study the "bipartitioning protocol"
where the two halves of a system initially prepared at different temperatures
are joined together and then left to evolve unitarily with the same
Hamiltonian. We identify two different limits in which the semiclassical
predictions are analytically recovered from GHD: a particular non-relativistic
limit and the low temperature regime. Interestingly, the transport of
topological charge becomes sub-ballistic in these cases. Away from these limits
we find that the semiclassical predictions are only approximate and, in
contrast to the latter, the transport is always ballistic. This statement seems
to hold true even for the so-called "hybrid" semiclassical approach, where
finite time DMRG simulations are used to describe the evolution in the internal
space.Comment: 30 pages, 6 figure
Quench dynamics of the Ising field theory in a magnetic field
We numerically simulate the time evolution of the Ising field theory after
quenches starting from the integrable model using the Truncated Conformal
Space Approach. The results are compared with two different analytic
predictions based on form factor expansions in the pre-quench and post-quench
basis, respectively. Our results clarify the domain of validity of these
expansions and suggest directions for further improvement. We show for quenches
in the model that the initial state is not of the integrable pair state
form. We also construct quench overlap functions and show that their
high-energy asymptotics are markedly different from those constructed before in
the sinh/sine-Gordon theory, and argue that this is related to properties of
the ultraviolet fixed point
Perturbative post-quench overlaps in Quantum Field Theory
In analytic descriptions of quantum quenches, the overlaps between the
initial pre-quench state and the eigenstates of the time evolving Hamiltonian
are crucial ingredients. We construct perturbative expansions of these overlaps
in quantum field theories where either the pre-quench or the post-quench
Hamiltonian is integrable. Using the Ising field theory for concrete
computations, we give explicit expressions for the overlaps up to second order
in the quench size, and verify our results against numerical results obtained
using the Truncated Conformal Space Approach. We demonstrate that the expansion
using the post-quench basis is very effective, but find some serious
limitations for the alternative approach using the pre-quench basis
Temperature driven quenches in the Ising model: appearance of negative RĂ©nyi mutual information
We study the dynamics of the transverse field Ising chain after a local quench
in which two independently thermalised chains are joined together and are left
to evolve unitarily. In the emerging non-equilibrium steady state the RĂ©nyi
mutual information with different indices are calculated between two adjacent
segments of the chain, and are found to scale logarithmically in the subsystem
size. Surprisingly, for RĂ©nyi indices > 2 we find cases where the prefactor of
the logarithmic dependence is negative. The fact that the naively defined RĂ©nyi
mutual information might be negative has been pointed out before, however, we
provide the first example for this scenario in a realistic many-body setup. Our
numerical and analytical results indicate that in this setup it can be negative for
any index > 2 while it is always positive for < 2. Interestingly, even for
> 2 the calculated prefactors show some universal features: for example, the
same prefactor is also shown to govern the logarithmic time dependence of the
RĂ©nyi mutual information before the system relaxes locally to the steady state.
In particular, it can decrease in the non-equilibrium evolution after the quench
Kibble-Zurek mechanism in the Ising Field Theory
The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp
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