C. Lavalle

Antiholons in one-dimensional t-J models.

Using a newly developed hybrid Monte Carlo algorithm for the nearest-neighbor (nn) t-J model, we show that antiholons identified in the supersymmetric inverse squared (IS) t-J model are clearly visible in the electron-addition spectrum of the nn t-J model at J=2t and also for J=0.5t, a value of experimental relevance.

Dynamics and Criticality of Correlated Electrons and Quantum Gases

Quantum Monte Carlo simulations are used to study the dynamics and the critical properties of strongly correlated systems relevant to the fields of cold quantum gasses and high-T c superconductivity. Recent advances in cooling techniques of quantum gasses allow to reach the degenerate regime for fermionic samples. Loading these systems on optical lattices can bring the gas to a strongly correlated regime. We analyze the properties of trapped degenerate Fermi gasses on optical lattices and show that they display quantum critical behavior and universality at the boundaries between metallic and Mott insulating phases. On our other field of interest, high-T c superconductivity, a Quantum Monte Carlo algorithm we developed recently is used to study the dynamics of the nearest-neighbor (n.n) t-J model relevant to the low energy properties of the copper oxides materials. We show that antiholons identified in the supersymmetric inverse squared (ISE) t-J model are generic excitation of the n.n. model since they are clearly visible in the single-particle spectral function of the n.n. t-J model in the whole Luttinger-liquid regime. We have further shown that even the analysis of the two-particle spectral functions of the n.n. t-J model can be based on the elementary excitations of the ISE t-J model.

Single Hole Dynamics in Correlated Insulators

We present recent quantum Monte Carlo results for two canonical model Hamiltonians of strongly correlated electrons, the t-J and the Kondo lattice models. Ground state properties on systems sizes up to 24 × 24 are computed numerically. Both models at a particular band filling are correlated insulators. Here, we concentrate on the dynamics of single hole doped into this state. For the t-J model we show that two-leg ladder systems can be well understood from a strong coupling limit along the rungs. In the three-leg ladder system, the low-energy spectrum can be described as an effective chain and an effective two-leg ladder for the symmetric and antisymmetric band, respectively. In the Kondo lattice model competing interactions-the Ruderman-Kittel-Kasuya-Yossida (RKKY) interaction and Kondo effect-lead to a quantum phase transition between ordered and disordered magnetic states. Analysis of the single-hole dispersion relation shows that the RKKY interaction and Kondo effects coexist: impurity spins are partially screened and the remnant magnetic moment orders.

Dynamical Properties of the t-J Model

We present a new quantum Monte Carlo method for the determination of the one-particle propagator in the t-J model. The method can be used both at zero doping, where it is free from the notorious sign problem, and at finite doping with holes. For one dimension we show, that a simple slave particle picture is able to describe the overall features of the spectral function at half filling. Additionally we give results at small doping. In two dimensions we observe a dispersion as predicted by self-consistent Born approximation. We observe flat bands at k = (π, 0), and a minimum of the dispersion at k = (π/2, π/2). We further show the existence of string excitations by considering the excitations above the quasiparticle peak at k ≈ (π/2, π/2). As opposed to from the one-dimensional case, the quasiparticle weight is finite in the thermodynamic limit in two dimensions.

Monte Carlo Simulations of Strongly Correlated and Frustrated Quantum Systems

We study the dynamics of the 1D t-J model with nearest neighbor (n.n) interaction at finite doping using the hybrid-loop quantum Monte Carlo. On the basis of the spectral functions of the 1/r 2 t-J model the excitation content for the one- and two-particle spectral functions for the n.n. t-J model are obtained from the Bethe-Ansatz solution and compared with the Monte Carlo results. We find that the procedure describes with extremely hight accuracy the excitation of the n.n. t-J model. We furthermore use quantum Monte Carlo simulations to analyze the phases of ultra-cold bosonic atom gases in optical lattices, in particular in the presence of frustrated and random interaction strength. We find that such systems display interesting quantum phases, such as supersolid and Bose-glass phases, and discuss possible experimental setups to examine such phenomena.

Numerical Simulations of Quantum Gases, Magnetic, and Correlated Electronic Systems

A variety of quantum Monte Carlo algorithms are used to study the equilibrium properties of strongly correlated quantum systems relevant to the fields of high-Tc superconductivity and magnetism. Furthermore, a new exact numerical method was developed and applied to strongly correlated quantum gases to unveil their universal properties in equilibrium and new states of matter out of equilibrium.

Quantum Monte-Carlo Simulations of Correlated Bosonic and Fermionic Systems

We review recent results of quantum Monte Carlo simulations applied to correlated electronic and bosonic systems. We concentrate on three subjects. 1) Using a recently developed hybrid quantum Monte-Carlo algorithm we investigate the excitation spectra of the one-dimensional t — J model. Our results give strong numerical support for the existence of antiholons, which along with spinons and holons correspond to the elementary excitations of this model. 2) Very recently, it was experimentally demonstrated, that it is possible to attain temperatures low enough, such that degenerate quantum gases can be studied in magneto-optical traps, the most prominent example being Bose-Einstein condensation of alkali atoms. Under the action of a periodic potential created by interfering laser beams, such systems can be brought to a strongly correlated state. We present numerical simulations in one-dimension in order to understand theses new states of matter. 3) Taking the step from one to two and three dimensions poses a formidable numerical challenge. In particular for fermionic models the quantum Monte Carlo method suffers from the so-called sign problem which renders simulations exponentially expensive in CPU time as a function of inverse temperature at lattice size. We show that by considering multi-flavored models this problem is reduced and in some special cases altogether removed.

Thermodynamics and Dynamics of Correlated Electron Systems

Based on state of the art Quantum Monte Carlo simulations, we investigate the metallic states of the one-dimensional t-J model and of a depleted Kondo lattice model in two dimensions. In the one-dimensional case, it is known that correlation effects invalidate the Fermi liquid picture and that the elementary excitations are spinons and holons carrying separately the charge and spin of the electron. In this dimension we will present new results on the single particle spectral function and discuss the implications of spin-charge separation on this quantity. The Kondo lattice model describes heavy fermion materials which generically have Fermi liquid ground states but with effective masses up to three orders of magnitude larger that the bare electron mass. On the basis of numerical simulations, we will show how this heavy fermion state comes about and set the emphasis on the coherence temperature.

Simulation of infinitely strongly interacting fermions from one to two dimensions

The limit of infinitely strong interaction is the relevant one for understanding the low energy sector of strongly correlated electronic systems like high-temperature superconductors and new related compounds like the so-called ladder materials. The t-J model is the generic one, where strong correlation is taken into account by projecting out doubly occupied sites. We present simulations for both the single-hole and finite doping cases of the t-J model performed with newly developed quantum Monte Carlo algorithms, in chains, ladders, and planes, where the spectral function and the quasiparticle weight are obtained.

Single Particle Excitations in the t-J Model

We present a new quantum Monte Carlo method for the determination of the oneparticle propagator in the t-J model. The method can be used both at zero doping, where it is free from the notorious sign problem, and at finite dopings. Here, we present results in two dimensions. As obtained by other numerical methods, we observe a dispersion as predicted by self-consistent Born approximation. We observe an extremely flat band at \( \vec k = (\pi ,0) \), and a minimum of the dispersion at \( \vec k = (\pi /2,\pi /2) \). We further show the existence of string excitations by considering the excitations above the quasiparticle peak at \( \vec k \approx (\pi /2,\pi /2) \). As opposed to the one-dimensional case, the quasiparticle weight is finite in the thermodynamic limit in two dimensions.