27 research outputs found
The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
We consider the transverse dynamical structure factor of the anisotropic
Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime
(). Specializing to the case of zero field, we use two independent
approaches based on integrability (one valid for finite size, the other for the
infinite lattice) to obtain the exact two-spinon part of this correlator. We
discuss in particular its asymmetry with respect to the momentum line,
its overall anisotropy dependence, and its contribution to sum rules.Comment: 19 pages, 6 figure
Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas
We consider the non-equilibrium dynamics of the interacting Lieb-Liniger gas
after instantaneously switching the interactions off. The subsequent time
evolution of the space- and time-dependent correlation functions is computed
exactly. Different relaxation behavior is observed for different correlation
functions. The long time average is compared with the predictions of several
statistical ensembles. The generalized Gibbs ensemble restricted to a fixed
number of particles is shown to give correct results at large times for all
length scales.Comment: 9 pages, 11 figure
Many-body localization and thermalization in the full probability distribution function of observables
We investigate the relation between thermalization following a quantum quench
and many-body localization in quasiparticle space in terms of the long-time
full distribution function of physical observables. In particular, expanding on
our recent work [E. Canovi {\em et al.}, Phys. Rev. B {\bf 83}, 094431 (2011)],
we focus on the long-time behavior of an integrable XXZ chain subject to an
integrability-breaking perturbation. After a characterization of the breaking
of integrability and the associated localization/delocalization transition
using the level spacing statistics and the properties of the eigenstates, we
study the effect of integrability-breaking on the asymptotic state after a
quantum quench of the anisotropy parameter, looking at the behavior of the full
probability distribution of the transverse and longitudinal magnetization of a
subsystem. We compare the resulting distributions with those obtained in
equilibrium at an effective temperature set by the initial energy. We find
that, while the long time distribution functions appear to always agree {\it
qualitatively} with the equilibrium ones, {\it quantitative} agreement is
obtained only when integrability is fully broken and the relevant eigenstates
are diffusive in quasi-particle space.Comment: 18 pages, 11 figure
Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
We consider the time evolution of order parameter correlation functions after
a sudden quantum quench of the magnetic field in the transverse field Ising
chain. Using two novel methods based on determinants and form factor sums
respectively, we derive analytic expressions for the asymptotic behaviour of
one and two point correlators. We discuss quenches within the ordered and
disordered phases as well as quenches between the phases and to the quantum
critical point. We give detailed account of both methods.Comment: 65 pages, 21 figures, some typos correcte
Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
We analyze quantum quenches in integrable models and in particular the
determination of the initial state in the basis of eigenstates of the
post-quench hamiltonian. This leads us to consider the set of transformations
of creation and annihilation operators that respect the Zamolodchikov-Faddeev
algebra satisfied by integrable models. We establish that the Bogoliubov
transformations hold only in the case of quantum quenches in free theories. In
the most general case of interacting theories, we identify two classes of
transformations. The first class induces a change in the S-matrix of the theory
but not of its ground state, whereas the second class results in a "dressing"
of the operators. As examples of our approach we consider the transformations
associated with a change of the interaction in the Sinh-Gordon and the
Lieb-Liniger model.Comment: v2: published version (typos corrected
Remarks on the notion of quantum integrability
We discuss the notion of integrability in quantum mechanics. Starting from a
review of some definitions commonly used in the literature, we propose a
different set of criteria, leading to a classification of models in terms of
different integrability classes. We end by highlighting some of the expected
physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2
R\ue9nyi entropies of generic thermodynamic macrostates in integrable systems
We study the behaviour of R\ue9nyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\ue9nyi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary R\ue9nyi entropies after the quench from the dimer and the tilted N\ue9el state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full detail the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies
Adjacent spin operator dynamical structure factor of the S = 1/2 Heisenberg chain
Considering the adjacent spin operators SjzSj + 1z and Sj − Sj + 1 − in the S = 1/2 Heisenberg chain, we give a determinant representation of their form factors. The dynamical structure factors of the respective operators are computed over the whole Brillouin zone in several magnetic fields and the resulting signal is analyzed in terms of excitation types. Among other results, we find that the SjzSj + 1z dynamical structure factor carries a large weight of the four-spinon excitations which are distinguishable from the two-spinon signal because they are located outside the two-spinon spectrum