arXiv subjects

Jean-Sebastien Caux

Publications and source records attributed to Jean-Sebastien Caux.

13 recordsLinked to original sources

arXiv2015

Complete Generalized Gibbs Ensemble in an interacting Theory

In integrable many-particle systems, it is widely believed that the stationary state reached at late times after a quantum quench can be described by a generalized Gibbs ensemble (GGE) constructed from their extensive number of conserved charges. A crucial issue is then to identify a complete set of these charges, enabling the GGE to provide exact steady state predictions. Here we solve this long-standing problem for the case of the spin-1/2 Heisenberg chain by explicitly constructing a GGE which uniquely fixes the macrostate describing the stationary behaviour after a general quantum quench. A crucial ingredient in our method, which readily generalizes to other integrable models, are recently discovered quasi-local charges. As a test, we reproduce the exact post-quench steady state of the Neel quench problem obtained previously by means of the Quench Action method.

quant-ph↗

arXiv2013

Interaction quenches in the 1D Bose gas

The non-equilibrium dynamics of integrable systems are special: there is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a Generalized Gibbs Ensemble (GGE). Most of the studies on the GGE so far have focused on models that can be mapped to quadratic systems while analytic treatment in non-quadratic systems remained elusive. We obtain results on interaction quenches in a non-quadratic continuum system, the 1D Bose gas described by the integrable Lieb-Liniger model. We compute local correlators for a non-interacting initial state and arbitrary final interactions as well as two-point functions for quenches to the Tonks-Girardeau regime. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble.

cond-mat.stat-mech↗

arXiv2013

Time evolution of local observables after quenching to an integrable model

We consider quantum quenches in integrable models. We argue that the behaviour of local observables at late times after the quench is given by their expectation values with respect to a single representative Hamiltonian eigenstate. This can be viewed as a generalization of the eigenstate thermalization hypothesis to quantum integrable models. We present a method for constructing this representative state by means of a generalized Thermodynamic Bethe Ansatz (GTBA). Going further, we introduce a framework for calculating the time dependence of local observables as they evolve towards their stationary values. As an explicit example we consider quantum quenches in the transverse-field Ising chain and show that previously derived results are recovered efficiently within our framework.

cond-mat.stat-mech↗

arXiv2013

Relaxation dynamics of conserved quantities in a weakly non-integrable one-dimensional Bose gas

In this work we report preliminary results on the relaxational dynamics of one dimensional Bose gases, as described by the Lieb-Liniger model, upon release from a parabolic trap. We explore the effects of integrability and integrability breaking upon these dynamics by placing the gas post-release in an integrability breaking one-body cosine potential of variable amplitude. By studying the post-quench evolution of the conserved charges that would exist in the purely integrable limit, we begin to quantify the effects of the weak breaking of integrability on the long time thermalization of the gas.

cond-mat.quant-gas↗

arXiv2011

Theory of superfluidity and drag force in the one-dimensional Bose gas

The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.

cond-mat.quant-gas↗

arXiv2011

The Spin-Exchange Dynamical Structure Factor of the S=1/2 Heisenberg Chain

We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect Resonant Inelastic X-ray Scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into *two spinon* states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.

cond-mat.str-el↗

arXiv2010

Dynamical correlation functions of the mesoscopic pairing model

We study the dynamical correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact expressions for the form factors of the most important observables. By summing these form factors over a relevant set of states, we obtain very precise estimates of the correlation functions, as confirmed by global sum-rules (saturation above 99% in all cases considered). Unlike the case of many other Bethe Ansatz solvable theories, simple two-particle states are sufficient to achieve such saturations, even in the thermodynamic limit. We provide explicit results at half-filling, and discuss their finite-size scaling behavior.

cond-mat.str-el↗

arXiv2009

Decay of superfluid currents in the interacting one-dimensional Bose gas

We examine the superfluid properties of a 1D Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.

cond-mat.quant-gas↗

arXiv2008

Quantum quenches from integrability: the fermionic pairing model

Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from both the vanishing time scale of the quench event, which can thus create arbitrarily high energy modes, and its non-local nature, which curtails the utility of local excitation bases. We here show that nonperturbative methods based on integrability can prove sufficiently powerful to completely characterize quantum quenches: we illustrate this using a model of fermions with pairing interactions (Richardson's model). The effects of simple (and multiple) quenches on the dynamics of various important observables are discussed. Many of the features we find are expected to be universal to all kinds of quench situations in atomic physics and condensed matter.

cond-mat.str-el↗

arXiv2007

Exact mesoscopic correlation functions of the pairing model

We study the static correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. Making use of the Algebraic Bethe Ansatz formalism, we obtain exact expressions which are easily evaluated numerically for any value of the pairing strength up to large numbers of particles. We provide explicit results at half-filling and extensively discuss their finite-size scaling behavior.

cond-mat.mes-hall↗

arXiv2006

One-particle dynamical correlations in the one-dimensional Bose gas

The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb-Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is well-adapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case.

cond-mat.stat-mech↗

arXiv2000

Andreev scattering and Josephson current in a one-dimensional electron liquid

Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are re-examined. We first present some apparently new results on the non-interacting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e. zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low energy properties of a junction (E<<Δ, the superconducting gap) can be obtained by "integrating out" the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization/renormalization group/boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interactions but to the Andreev one for attractive interactions. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior.

cond-mat.supr-con↗

arXiv1998

Exact Multifractality for Disordered N-Flavour Dirac Fermions in Two Dimensions

We present a nonperturbative calculation of all multifractal scaling exponents at strong disorder for critical wavefunctions of Dirac fermions interacting with a non-Abelian random vector potential in two dimensions. The results, valid for an arbitrary number of fermionic flavours, are obtained by deriving from Conformal Field Theory an effective Gaussian model for the wavefunction amplitudes and mapping to the thermodynamics of a single particle in a random potential. Our spectrum confirms that the wavefunctions remain delocalized in the presence of strong disorder.

cond-mat.dis-nn↗