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 ($\Delta > 1$). 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 $\pi/2$ 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