arXiv subjects

Marcos Rigol

Publications and source records attributed to Marcos Rigol.

At least 163 records · Page 9Linked to original sources

arXiv2007

Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis through a thorough ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].

cond-mat.other↗

arXiv2006

Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes

We study the ground-state properties and nonequilibrium dynamics of hard-core bosons confined in one-dimensional lattices in the presence of an additional periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed after a sudden switch-on or switch-off of the superlattice potential, which can bring the system into insulating or superfluid phases, respectively. A collapse and revival of the zero-momentum peak can be seen in the first case. We study in detail the relaxation of these integrable systems towards equilibrium. We show how after relaxation time averages of physical observables, like the momentum distribution function, can be predicted by means of a generalization of the Gibbs distribution.

cond-mat.other↗

arXiv2006

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagomé}, triangular, and square lattices.

cond-mat.str-el↗

arXiv2005

Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.

cond-mat.str-el↗

arXiv2005

Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices

We present an exact study of the finite-temperature properties of hard-core bosons (HCB's) confined on one-dimensional optical lattices. Our solution of the HCB problem is based on the Jordan-Wigner transformation and properties of Slater determinants. We analyze the effects of the temperature on the behavior of the one-particle correlations, the momentum distribution function, and the lowest natural orbitals. In addition, we compare results obtained using the grand-canonical and canonical descriptions for systems like the ones recently achieved experimentally. We show that even for such small systems, as small as 10 HCB's in 50 lattice sites, there are only minor differences between the energies and momentum distributions obtained within both ensembles.

cond-mat.stat-mech↗

arXiv2005

Gauge invariance properties and singularity cancellations in a modified PQCD

The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $α$. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $α$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.

hep-ph↗

arXiv2005

Free expansion of impenetrable bosons on one-dimensional optical lattices

We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of noninteracting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with the one of noninteracting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.

cond-mat.stat-mech↗

arXiv2005

Ground-state properties of hard-core bosons confined on one-dimensional optical lattices

We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.

cond-mat.stat-mech↗

arXiv2005

Fermionization in an expanding 1D gas of hard-core bosons

We show by means of an exact numerical approach that the momentum distribution of a free expanding gas of hard-core bosons on a one-dimensional lattice approaches to the one of noninteracting fermions, acquiring a Fermi edge. Yet there is a power-law decay of the one-particle density matrix $ρ_x\sim 1/\sqrt{x}$, as usual for hard-core bosons in the ground state, which accounts for a large occupation of the lowest natural orbitals for all expansion times. The fermionization of the momentum distribution function, which is not observed in equilibrium, is analyzed in detail.

cond-mat.stat-mech↗

arXiv2004

Numerical simulations of strongly correlated fermions confined in 1D optical lattices

On the basis of quantum Monte Carlo (QMC) simulations we study the formation of Mott domains in the one-dimensional Hubbard model with an additional confining potential. We find evidences of quantum critical behavior at the boundaries of the Mott-insulating regions. A local compressibility defined to characterize the local phases exhibits a non-trivial critical exponent on entering the Mott-insulating domains. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We also study the momentum distribution function of the trapped system, and determine its phase diagram.

cond-mat.str-el↗

arXiv2004

Emergence of quasi-condensates of hard-core bosons at finite momentum

An exact treatment of the non-equilibrium dynamics of hard-core bosons on one-dimensional lattices shows that, starting from a pure Fock state, quasi-long-range correlations develop dynamically, and that they lead to the formation of quasi-condensates at finite momenta. Scaling relations characterizing the quasi-condensate and the dynamics of its formation are obtained. The relevance of our findings for atom lasers with full control of the wave-length by means of a lattice is discussed.

cond-mat.stat-mech↗

arXiv2004

Confinement control by optical lattices

It is shown that the interplay of a confining potential with a periodic potential leads for free particles to states spatially confined on a fraction of the total extension of the system. A more complex `slicing' of the system can be achieved by increasing the period of the lattice potential. These results are especially relevant for fermionic systems, where interaction effects are in general strongly reduced for a single species at low temperatures.

cond-mat.stat-mech↗

arXiv2004

Universal properties of hard-core bosons confined on one-dimensional lattices

Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation $λ_η$ of the natural orbitals for large-$η$ at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.

cond-mat.stat-mech↗

arXiv2004

Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices

Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulator transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.

cond-mat.str-el↗

arXiv2003

Hadron spectra from a non-relativistic model with confining harmonic potential

Hadron spectra and other properties of quark systems are studied in the framework of a non-relativistic spin-independent phenomenological model. The chosen confining potential is harmonic, which allowed us to obtain analytical solutions for both meson and baryon (of equal constituent quarks) spectra. The introduced parameters are fixed from the low-lying levels of heavy quark mesons. The requirement of flavor independence is imposed, and it restricts the possible choices of inter-quark potentials. The hyper-spherical coordinates are considered for the solution of the three-body problem.

physics.ed-ph↗

arXiv2002

Constituent quark masses from a modified perturbative QCD

A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in the first approximations. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input consists in that is evaluated up to order g^2 as a function of the unique parameter C defining the modified propagator and then C is fixed to give a current estimate of . The light quarks u and d result to be confined and the s, c, b and t ones show damped propagation modes, then suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On another hand, the condensate effects on the gluon self-energy furnish a tachionic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD.

hep-ph↗

arXiv2001

Gluon, Quark and Hadron Masses from a Modified Perturbative QCD

The development of a Modified Perturbation Theory for QCD, introduced in previous works, is continued. The gluon propagator is modified as consequence of a soft gluon pairs condensate in the vacuum. The modified Feynman rules for $α=1$ are shown, and some physical magnitudes calculated with them. The mean value of $G^{2}$, gluon masses and the effective potential are calculated up to the $g^2$ order, improving previous calculations. In connection with the gluon self-energy it follows that the gluonic mass shell becomes tachyonic in the considered approximation. The constituent quarks masses, produced by the influence of the condensate, are also calculated. Results of the order of 1/3 of the nucleon mass, are obtained for the constituent masses of the up and down quarks. In addition, the predicted flavour dependence of the calculated quarks masses turns out to be the appropriate to reproduce the spectrum of the ground states within the various groups of hadronic resonances, through the simple addition of their constituent quark masses. Finally, the generalization of the theory for arbitrary values of the $α$ gauge parameter is explored.

hep-ph↗

arXiv2001

About an Alternative Vacuum State for Perturbative QCD

A particular initial state for the construction of a perturbative QCD expansion is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global $SU(3)$ symmetries. The general form of the Wick theorem is discussed, and it follows that the gluon and ghost propagators determined by the proposed vacuum state, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work, and reviewed here. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. A brief review of the canonical quantization for gauge fields, developed by Kugo and Ojima, is done and the value of the gauge parameter $α$ is fixed to $α=1$ where the procedure is greatly simplified. Therefore, after assuming that the adiabatic connection of the interaction does not take out the state from the interacting physical space, the predictions of the perturbation expansion for the physical quantities, at the value $α=1$, should have meaning. The validity of this conclusion solves the gauge dependence indeterminacy remained in the proposed perturbation expansion.

hep-th↗