arXiv subjects

Guillaume Roux

Publications and source records attributed to Guillaume Roux.

30 records · Page 2Linked to original sources

arXiv2013

Localization of spinons in random Majumdar-Ghosh chains

We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh (RMG) point. There, spinons are almost independent, remain gapped, and localize in Lifshitz states whose localization length is analytically obtained. The RMG point then displays a quantum phase transition to phase of localized spinons at large disorder. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.

cond-mat.str-el↗

arXiv2012

Entangling many-body bound states with propagative modes in Bose-Hubbard systems

The quantum evolution of a cloud of bosons initially localized on part of a one dimensional optical lattice and suddenly subjected to a linear ramp is studied, realizing a quantum analog of the "Galileo ramp" experiment. The main remarkable effects of this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-like oscillations around a plateau. This setup, by coupling bound states to propagative modes, creates two diverging condensates for which the entanglement is computed and related to the equilibrium one. Further, we address the role of integrability on the entanglement and on the damping and thermalization of simple observables.

cond-mat.quant-gas↗

arXiv2011

Slow quench dynamics of Mott-insulating regions in a trapped Bose gas

We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased, and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly whereas long range correlations require longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy, and their respective currents, the local compressibility, the local excess energy, the heat and single particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization group technique and comparisons with time-evolutions done within the Gutzwiller approximation are provided.

cond-mat.quant-gas↗

arXiv2011

Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.

cond-mat.str-el↗

arXiv2011

Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice

We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the non-trivial scaling of the energy absorbed with the ramp time.

cond-mat.quant-gas↗

arXiv2011

Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator - Luttinger liquid - Bose glass

One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depends on the so-called Jordan-Wigner string, real-space observables are similar for free-fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed, and leads to a totally different physics between free-fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but non-trivial model of hard-core bosons hopping in a two-leg ladder geometry. At half-filling, while a band insulator appears for fermions at large interchain hopping tperp >2t only, a Mott gap opens up for bosons as soon as tperp\neq0 through a Kosterlitz-Thouless transition. Away from half-filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a non-trivial filling-dependent Luttinger parameter 1/2\leq Ks \leq 1. Consequences for experiments in cold atoms, spin ladders in a magnetic field, as well as disorder effects are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a 1D superfluid and an insulating Bose glass phase.

cond-mat.str-el↗

arXiv2011

Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model

We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multi-particle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the novel phase. The effective physics of the trimer gas is as well studied. Lastly, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

cond-mat.quant-gas↗

arXiv2010

Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''

In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expected thermalization scenario discussed by Rigol. In addition, we emphasize a few other important aspects, in particular the definition of temperature and the equivalence of ensemble, which are much more difficult to show numerically even though we believe they are essential to the discussion of thermalization. These remarks could be of interest to people interested in the interpretation of the data obtained on finite-size systems.

cond-mat.quant-gas↗

arXiv2010

Statistical properties of the spectrum the extended Bose-Hubbard model

Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the ratio of adjacent level spacings, useful at large interaction, to distinguish between chaotic and non-chaotic regimes. After revisiting the bare Bose-Hubbard model, we study the effect of two different perturbations: next-nearest neighbor hopping and nearest-neighbor interaction. The system size dependence is investigated together with the effect of the proximity to integrable points or lines. Lastly, we discuss the consequences of a cutoff in the number of onsite bosons onto the level statistics.

cond-mat.quant-gas↗

arXiv2010

Pair Density Waves in coupled doped two-leg Ladders

Motivated by Resonant X-ray scattering experiments in cuprate ladder materials showing charge order modulation of period $λ=3$ and 5 at specific hole densities, we investigate models involving the electronic t-J ladders and bosonic chains coupled via screened Coulomb repulsion. Extensive density matrix renormalization group calculations applied to the ladders/chains supplemented by a self-consistent mean-field treatment of the inter-ladder/chain coupling provide quantitative estimates of the charge order for $λ=3,4$ and 5. As previously proposed, such patterns correspond to the emergence of pair density waves which stem from the strong electronic correlations. We comment on the existence of a $λ=4$ modulation not seen so far in experiment.

cond-mat.str-el↗

arXiv2010

Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model

We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground-states. Both criteria can be computed using ground-state techniques that work for larger system sizes than full spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap which frequency is quenched, and the one-dimensional Bose-Hubbard model, that is known to be non-integrable and for which recent studies have uncovered remarkable non-equilibrium behaviors. The diagonal weights of the time-averaged density-matrix are computed and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the "thermalized" regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite size effects that render difficult a thorough comparison with statistical ensembles. In addition, we show that the non-thermalized regime, emerging on finite size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the non-interacting limit to the atomic limit.

cond-mat.quant-gas↗

arXiv2009

Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined

When a quantum many-body system undergoes a quench, the time-averaged density-matrix $ρ$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium predictions. We show that the weights of $ρ$ can be efficiently computed with Lanczos diagonalization for relatively large Hilbert spaces. As an application, we investigate the crossover from perturbative to non-perturbative quenches in the non-integrable Bose-Hubbard model: on finite systems, an approximate Boltzmann distribution is observed for small quenches, while for larger ones the distributions do not follow standard equilibrium predictions. Studying thermodynamical features, such as the energy fluctuations and the entropy, shows that $ρ$ bears a memory of the initial state.

cond-mat.str-el↗