Quasiparticle Dynamics in the Kondo Lattice Model at Half Filling

We study spectral properties of quasiparticles in the Kondo lattice model in one and two dimensions including the coherent quasiparticle dispersions, their spectral weights and the full two-quasiparticle spectrum using a cluster expansion scheme. We investigate the evolution of the quasiparticle band as antiferromagnetic correlations are enhanced towards the RKKY limit of the model. In both the 1D and the 2D model we find that a repulsive interaction between quasiparticles results in a distinct antibound state above the two-quasiparticle continuum. The repulsive interaction is correlated with the emerging antiferromagnetic correlations and can therefore be associated with spin fluctuations. On the square lattice, the antibound state has an extended s-wave symmetry.Comment: 8 pages, 11 figure

Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations

We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be O([N log N]^2) for both the ferromagnetic and the fully frustrated 2D Ising model with N spins. Our new algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.Comment: 6 pages, 5 figure

Ramping fermions in optical lattices across a Feshbach resonance

We study the properties of ultracold Fermi gases in a three-dimensional optical lattice when crossing a Feshbach resonance. By using a zero-temperature formalism, we show that three-body processes are enhanced in a lattice system in comparison to the continuum case. This poses one possible explanation for the short molecule lifetimes found when decreasing the magnetic field across a Feshbach resonance. Effects of finite temperatures on the molecule formation rates are also discussed by computing the fraction of double-occupied sites. Our results show that current experiments are performed at temperatures considerably higher than expected: lower temperatures are required for fermionic systems to be used to simulate quantum Hamiltonians. In addition, by relating the double occupancy of the lattice to the temperature, we provide a means for thermometry in fermionic lattice systems, previously not accessible experimentally. The effects of ramping a filled lowest band across a Feshbach resonance when increasing the magnetic field are also discussed: fermions are lifted into higher bands due to entanglement of Bloch states, in good agreement with recent experiments.Comment: 9 pages, 7 figure

Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions

We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases. Here, we address systems in two spatial dimensions and report on the behavior of Ising and Fibonacci anyons under the numerical strong-disorder renormalization group (SDRG). In order to manage the topology-dependent interactions generated during the flow, we introduce a planar approximation to the SDRG treatment. We characterize this planar approximation by studying the flow of disordered hard-core bosons and the transverse field Ising model, where it successfully reproduces the known infinite randomness critical point with exponent \psi ~ 0.43. Our main conclusion for disordered anyon models in two spatial dimensions is that systems of Ising anyons as well as systems of Fibonacci anyons do not realize infinite randomness phases, but flow back to weaker disorder under the numerical SDRG treatment.Comment: 12 pages, 12 figures, 1 tabl

Two-dimensional quantum liquids from interacting non-Abelian anyons

A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.Comment: 5 pages, 6 figure

Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass

We investigate the performance of flat-histogram methods based on a multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional +/- J spin glass by measuring round-trip times in the energy range between the zero-temperature ground state and the state of highest energy. Strong sample-to-sample variations are found for fixed system size and the distribution of round-trip times follows a fat-tailed Frechet extremal value distribution. Rare events in the fat tails of these distributions corresponding to extremely slowly equilibrating spin glass realizations dominate the calculations of statistical averages. While the typical round-trip time scales exponential as expected for this NP-hard problem, we find that the average round-trip time is no longer well-defined for systems with N >= 8^3 spins. We relate the round-trip times for multicanonical sampling to intrinsic properties of the energy landscape and compare with the numerical effort needed by the genetic Cluster-Exact Approximation to calculate the exact ground state energies. For systems with N >= 8^3 spins the simulation of these rare events becomes increasingly hard. For N >= 14^3 there are samples where the Wang-Landau algorithm fails to find the true ground state within reasonable simulation times. We expect similar behavior for other algorithms based on multicanonical sampling.Comment: 9 pages, 12 figure

Diffusion in the Continuous-Imaginary-Time Quantum World-Line Monte Carlo Simulations with Extended Ensembles

The dynamics of samples in the continuous-imaginary-time quantum world-line Monte Carlo simulations with extended ensembles are investigated. In the case of a conventional flat ensemble on the one-dimensional quantum S=1 bi-quadratic model, the asymmetric behavior of Monte Carlo samples appears in the diffusion process in the space of the number of vertices. We prove that a local diffusivity is asymptotically proportional to the number of vertices, and we demonstrate the asymmetric behavior in the flat ensemble case. On the basis of the asymptotic form, we propose the weight of an optimal ensemble as $1/\sqrt{n}$, where $n$ denotes the number of vertices in a sample. It is shown that the asymmetric behavior completely vanishes in the case of the proposed ensemble on the one-dimensional quantum S=1 bi-quadratic model.Comment: 4 pages, 2 figures, update a referenc

Generalized Ensemble and Tempering Simulations: A Unified View

From the underlying Master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the form of a one-dimensional Fokker-Planck equation or a hopping process on a one-dimensional chain. In particular, we discuss the conditions under which these representations are valid approximate Markovian descriptions of the random walk in order parameter or control parameter space. They allow a unified discussion of the stationary distribution on, as well as of the stationary flow across each space. We demonstrate that optimizing the flow is equivalent to minimizing the first passage time for crossing the space, and discuss the consequences of our results for optimizing simulations. Finally, we point out the limitations of these representations under conditions of broken ergodicity.Comment: 11 pages Latex, 2 eps figures, revised version, typos corrected, PRE in pres

Boundaries, Cusps and Caustics in the Multimagnon Continua of 1D Quantum Spin Systems

The multimagnon continua of 1D quantum spin systems possess several interesting singular features that may soon be accessible experimentally through inelastic neutron scattering. These include cusps and composition discontinuities in the boundary envelopes of two-magnon continuum states and discontinuities in the density of states, "caustics", on and within the continuum, which will appear as discontinuities in scattering intensity. In this note we discuss the general origins of these continuum features, and illustrate our results using the alternating Heisenberg antiferromagnetic chain and two-leg ladder as examples.Comment: 18 pages, 10 figure

Deconfinement Transition and Bound States in Frustrated Heisenberg Chains: Regimes of Forced and Spontaneous Dimerization

We use recently developed strong-coupling expansion methods to study the two-particle spectra for the frustrated alternating Heisenberg model, consisting of an alternating nearest neighbor antiferromagnetic exchange and a uniform second neighbor antiferromagnetic exchange. Starting from the limit of weakly coupled dimers, we develop high order series expansions for the effective Hamiltonian in the two-particle subspace. In the limit of a strong applied dimerization, we calculate accurately various properties of singlet and triplet bound states and quintet antibound states. We also develop series expansions for bound state energies in various sectors, which can be extrapolated using standard methods to cases where the external bond-alternation goes to zero. We study the properties of singlet and triplet bound states in the latter limit and suggest a crucial role for the bound states in the unbinding of triplets and deconfinement of spin-half excitations.Comment: 17 figures, revte