Lorenzo Piroli

Relaxation dynamics of local observables in integrable systems

We show, using the quench action approach (Caux and Essler 2013 Phys. Rev. Lett. 110 257203), that the whole post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient s 0 ψ (λ). This function can be extracted from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state. For a generic global quench the shape of s 0 ψ (λ) in the low momentum limit directly gives the exponent for the power law decay to the effective steady state. As an example we compute the time evolution of the static density-density correlation in the interacting Lieb-Liniger gas after a quench from a Bose-Einstein condensate. This shows an approach to equilibrium with power law t −3 which turns out to be independent of the post-quench interaction and of the considered observable.

Multiparticle Bound-State Formation following a Quantum Quench to the One-Dimensional Bose Gas with Attractive Interactions.

We consider quantum quenches from an ideal Bose condensate to the Lieb-Liniger model with an arbitrary attractive interaction strength. We focus on the properties of the stationary state reached at late times after the quench. Using recently developed methods based on integrability, we obtain an exact description of the stationary state for a large number of bosons. A distinctive feature of this state is the presence of a hierarchy of multiparticle bound states. We determine the dependence of their densities on interaction strength and obtain an exact expression for the stationary value of the local pair correlation g_{2}. We discuss ramifications of our results for cold atom experiments.

Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions

We consider quantum quenches to the sinh-Gordon integrable quantum field theory from a particular class of initial states. Our analysis includes the case of mass and interaction quenches starting from a non-interacting theory. By means of the recently developed quench action method, we fully characterize the stationary state reached at long times after the quench in terms of the corresponding rapidity distribution. We also provide exact results for the expectation values of arbitrary vertex operators in the post-quench stationary state by proposing a formula based on the analogy with the standard thermodynamic Bethe ansatz. Finally, we comment on the behavior of the post-quench stationary state under the mapping between the sinh-Gordon field theory and the one-dimensional Lieb-Liniger model.

Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal non-ballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of tDMRG simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.

Exact steady states for quantum quenches in integrable Heisenberg spin chains

What is the long-time behavior of a quantum system after it is brought out of equilibrium? In a generic case, it has been proposed that an effective thermalization occurs, and the local properties of the system can then be described by a thermal Gibbs ensemble. However, in integrable systems, with infinitely many conservation laws, the answer is far more complicated. It was shown in several special cases that the long-time steady state can be exactly described by the so called complete generalized Gibbs ensemble. The latter can be obtained by maximizing the entropy with constraints imposed by the conservation of energy, but also by additional carefully chosen subset of the integrals of motion. In this work, the authors analyze more general initial states, focusing on integrable XXZ Heisenberg spin chains. They find that the complete generalized Gibbs ensemble indeed correctly describes the system at long times after the quench.

Quantum quenches to the attractive one-dimensional Bose gas: exact results

We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function

Quasi-local conserved charges and spin transport in spin-1 integrable chains

g_2

Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

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Correlations and diagonal entropy after quantum quenches in XXZ chains

We consider the integrable one-dimensional spin-

What is an integrable quench

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