Dragi Karevski

Exact matrix product solution for the boundary-driven Lindblad XXZ chain.

We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix where the matrices satisfy a quadratic algebra. This algebra turns out to be related to the quantum algebra U(q)[SU(2)]. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to nonvanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.

Entanglement evolution after connecting finite to infinite quantum chains

We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.

Quantum quench from a thermal tensor state: Boundary effects and generalized Gibbs ensemble

We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size L is initially prepared into two halves L ([-L/2,0]) and R ([0, L/2]), each of them thermalized at two different temperatures T-L and T-R, respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system (L -> infinity), we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.

Off equilibrium dynamics in the 2d-XY system

We study the non-equilibrium time evolution of the classical XY spin model in two dimensions. The two-time autocorrelation and linear response functions are considered for systems initially prepared in a high temperature state and in a completely ordered state. After a quench into the critical phase, we use Monte Carlo simulations to determine the time-evolution of these quantities, and we deduce the temperature dependence of the slope of the parametric plot susceptibility/correlation in the asymptotic regime. This slope is usually identified with the infinite fluctuation-dissipation ratio, which measures the extent of violation of the equilibrium fluctuation-dissipation theorem. However, a direct measure of this ratio leads to a vanishing value.

Relaxation in the XX quantum chain

We present the results obtained on the magnetization relaxation properties of an XX quantum chain in a transverse magnetic field. We first consider an initial thermal kink-like state where half of the chain is initially thermalized at a very high temperature Tb while the remaining half, called the system, is put at a lower temperature Ts. From this initial state, we derive analytically the Green function associated with the dynamical behaviour of the transverse magnetization. Depending on the strength of the magnetic field and on the temperature of the system, different regimes are obtained for the magnetic relaxation. In particular, with an initial droplet-like state, that is a cold subsystem of the finite size in contact at both ends with an infinite temperature environment, we derive analytically the behaviour of the time-dependent system magnetization.

Finite-size effects in layered magnetic systems

Thermal and magnetic effects in a system consisting of thin layers of coupled Ising spins with

Driven isotropic Heisenberg spin chain with arbitrary boundary twisting angle: exact results.

S=1/2

Critical quench dynamics in confined systems.

and

Probability distributions of the work in the two-dimensional Ising model

S=1

Random and aperiodic quantum spin chains: A comparative study

are considered. The specific heat and the correlation length display maxima at two different temperatures. It is discussed in what sense these maxima can be interpreted as a finite-size rounding of a thermodynamic singularity associated with a phase transition. The connection with ordinary, extraordinary and special surface phase transitions is made. In