Beat Ammon

Parallel Object Oriented Monte Carlo Simulations

We discuss the parallelization and object-oriented implementation of Monte Carlo simulations for physical problems. We present a C++ Monte Carlo class library for the automatic parallelization of Monte Carlo simulations. Besides discussing the advantages of object-oriented design in the development of this library, we show examples how C++ template techniques have allowed very generic but still optimal algorithms to be implemented for wide classes of problems. These parallel and object-oriented codes have allowed us to perform the largest quantum Monte Carlo simulations ever done in condensed matter physics.

Susceptibility and low-temperature thermodynamics of spin-1/2 Heisenberg ladders.

The temperature dependence of the uniform susceptibility and the ground-state energy of antiferromagnetic Heisenberg ladders with up to six legs has been calculated, using the Monte Carlo loop algorithm. The susceptibilities of even-leg ladders show spin gaps while those of odd-leg ladders remain finite in the zero-temperature limit. For small ratios of intra- to interleg couplings, odd-leg ladders can be mapped at low temperatures to single chains. For equal couplings, the logarithmic corrections at low temperatures increase markedly with the number of legs.

Effect of the three-site hopping term on the t-J model.

We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional {ital t}-{ital J} model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the {ital t}-{ital J} and Hubbard models. Phase separation, which exists in the {ital t}-{ital J} model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values {ital J}/{ital t}{lt}2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at {ital J}/{ital t}{gt}2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.

THERMODYNAMICS OF THE T-J LADDER : A STABLE FINITE-TEMPERATURE DENSITY MATRIX RENORMALIZATION GROUP CALCULATION

Accurate numerical simulations of a doped t-J model on a two-leg ladder are presented for the particle number, chemical potential, magnetic susceptibility and entropy in the limit of large exchange coupling on the rung using a finite temperature density matrix renormalization group (TDMRG) method. This required an improved algorithm to achieve numerical stability down to low temperatures. The thermal dissociation of hole pairs and of the rung singlets are separately observed and the evolution of the hole pair binding energy and magnon spin gap with hole doping is determined.

Thermodynamics of random ferromagnetic-antiferromagnetic spin-1/2 chains

Using the quantum Monte Carlo Loop algorithm, we calculate the temperature dependence of the uniform susceptibility, the specific heat, the correlation length, the generalized staggered susceptibility and magnetization of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in all the quantities and support strongly the conjecture drawn from the approximate real-space renormalization group treatment.A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.

Thermodynamic Properties of the One-Dimensional Kondo Insulators Studied by the Density Matrix Renormalization Group Method

Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T =0.1 t for various exchange constants. The obtained results clearly indicate crossover behavior from the high-temperature regime of nearly independent localized spins and conduction electrons to the low-temperature regime where the two degrees of freedom couple strongly. The low-temperature energy scales of the charge and spin susceptibilities are determined and are equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.

Doped Two Orbital Chains with Strong Hund's Rule Couplings - Ferromagnetism, Spin Gap, Singlet and Triplet Pairings

Different models for doping of two-orbital chains with mobile S =1/2 fermions and strong, ferromagnetic (FM) Hunds rule couplings stabilizing the S =1 spins are investigated by density matrix reno...

Spin-1 chain doped with mobile S = 1/2 fermions

We investigate the doping of a two-orbital chain with mobile S = 1/2 fermions as a valid model for Y2-xCaxBaNiO5. The S = 1 spins are stabilized by strong, ferromagnetic Hunds rule couplings. We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Gapless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the S = 1 chain accompanied by a finite string order parameter.

Monte Carlo study of the separation of energy scales in quantum spin 1/2 chains with bond disorder

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as Sr 3 CuPt 1- x Ir x O 6 . We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of Sr 3 CuPt 1- x Ir x O 6 by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.

QUANTUM MONTE CARLO LOOP ALGORITHM FOR THE T-J MODEL

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local algorithms. The method is completely ergodic and can be formulated directly in continuous time. We introduce improved estimators for simulations with a local sign problem. Some first results of finite temperature simulations are presented for a t-J chain, a frustrated Heisenberg chain, and t-J ladder models.