Márton Kormos

Correlations after quantum quenches in the XXZ spin chain: failure of the generalized Gibbs ensemble.

We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Néel states as initial states. We investigate numerically various short-ranged spin correlators in the long-time limit and find that they deviate significantly from predictions based on the generalized Gibbs ensemble (GGE) hypotheses. By computing the asymptotic spin correlators within the recently proposed quench-action formalism [Phys. Rev. Lett. 110, 257203 (2013)], however, we find excellent agreement with the numerical data. We, therefore, conclude that the GGE cannot give a complete description even of local observables, while the quench-action formalism correctly captures the steady state in this case.

Analytic results for a quantum quench from free to hard-core one-dimensional bosons

It is widely believed that the stationary properties after a quantum quench in integrable systems can be described by a generalized Gibbs ensemble (GGE), even if all the analytical evidence is based on free theories in which the pre- and post-quench modes are linearly related. In contrast, we consider the experimentally relevant quench of the one-dimensional Bose gas from zero to infinite interaction, in which the relation between modes is nonlinear, and consequently Wicks theorem does not hold. We provide exact analytical results for the time evolution of the dynamical density-density correlation function at any time after the quench and we prove that its stationary value is described by a GGE in which Wicks theorem is restored.

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 von Neumann entanglement entropies are found to be extensive, and the latter coincides with the thermodynamic entropy of the generalized Gibbs ensemble (GGE). 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 cumulants of the particle-number fluctuations. We also compare the extensive part of the entanglement entropy with the thermodynamic ones, showing that the GGE entropy equals the entanglement one and it is twice the diagonal entropy.

Interaction quench in a trapped 1D Bose gas

We studied the non-equilibrium quench dynamics from free to hard-core 1D bosons in the presence of a hard-wall confining potential. The density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution was characterised. It was found that for long times the system relaxes to a uniform density profile, but the correlation function memorises the initial state with a stationary algebraic long-distance decay, which is opposite to the exponential behaviour found for the same quench in the periodic setup. We also compute the stationary bosonic two-point correlator which was found to decay exponentially for large distances. A two-step mechanism was shown to govern the time evolution; a quick approach to an almost stationary value was followed by a slow algebraic relaxation to the true stationary state.

Real-time confinement following a quantum quench to a non-integrable model

Confinement plays an important role in many-body physics from high energy to condensed matter. New results show that it strongly affects the non-equilibrium dynamics after a quantum quench with possible implications from ultracold atoms to QCD.

Stationary entropies after a quench from excited states in the Ising chain

We consider the asymptotic state after a sudden quench of the magnetic field in the transverse field quantum Ising chain starting from excited states of the pre-quench Hamiltonian. We compute the thermodynamic entropies of the generalised Gibbs and the diagonal ensembles and we find that the generalised Gibbs entropy is always twice the diagonal one. We show that particular care should be taken in extracting the thermodynamic limit since different averages of equivalent microstates give different results for the entropies.

Hamiltonian truncation approach to quenches in the Ising field theory

In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan-Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we compute analytically the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.

From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation

We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two-point correlation function of the sine-Gordon theory is related to the generating function of the height distribution of the KPZ field with droplet initial conditions, i.e. the directed polymer free energy with two endpoints fixed. As shown recently, the latter can be expressed as a Fredholm determinant which in the large-time separation limit converges to the GUE Tracy-Widom cumulative distribution. Possible applications and extensions are discussed.