On the determinant representations of Gaudin models' scalar products and form factors

We propose alternative determinant representations of certain form factors and scalar products of states in rational Gaudin models realized in terms of compact spins. We use alternative pseudo-vacuums to write overlaps in terms of partition functions with domain wall boundary conditions. Contrarily to Slavnovs determinant formulas, this construction does not require that any of the involved states be solutions to the Bethe equations; a fact that could prove useful in certain non-equilibrium problems. Moreover, by using an atypical determinant representation of the partition functions, we propose expressions for the local spin raising and lowering operators form factors which only depend on the eigenvalues of the conserved charges. These eigenvalues define eigenstates via solutions of a system of quadratic equations instead of the usual Bethe equations. Consequently, the current work allows important simplifications to numerical procedures addressing decoherence in Gaudin models.Comment: 15 pages, 0 figures, Published versio

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

Stationary entanglement entropies following an interaction quench in 1D Bose gas

We analyze the entanglement properties of the asymptotic steady state after a quench from free to hard-core bosons in one dimension. The Renyi and on Neumann entanglement entropies are found to be extensive, and the latter coincides with the thermodynamic entropy of the generalized Gibbs ensemble (GCE). Computing the spectrum of the two-point function, we provide exact analytical results for both the leading extensive parts and the subleading terms for the entropies as well as for the cumutlants of the particle-number fluctuations. We also compare the extensive part of the entanglement entropy with the thermodynamic ones. showing that the GCE entropy equals the entanglement, one and it is twice the diagonal entropy

Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap

We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many-body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to stationary behavior at late times. We also describe the time dependence of the entanglement entropy which attains a very simple form in the stationary state

Exact solution for the quench dynamics of a nested integrable system

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model