Showing papers by "Matthias Troyer published in 2003"
TL;DR: A generalization of the classical Wang-Landau algorithm to quantum systems, which is efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transition, and allow the direct calculation of the free energy and entropy.
Abstract: We present a generalization of the classical Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] to quantum systems. The algorithm proceeds by stochastically evaluating the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order. Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct calculation of the free energy and entropy.
94 citations
TL;DR: The two-dimensional SU(N) quantum antiferromagnet, a generalization of the quantum Heisenberg model, is investigated by quantum Monte Carlo simulations and shows the absence of the intermediate spin-liquid phase.
Abstract: The two-dimensional $\mathrm{S}\mathrm{U}(N)$ quantum antiferromagnet, a generalization of the quantum Heisenberg model, is investigated by quantum Monte Carlo simulations. The ground state for $N\ensuremath{\le}4$ is found to be of the N\'eel type with broken $\mathrm{S}\mathrm{U}(N)$ symmetry, whereas it is of the Spin-Peierls type for $N\ensuremath{\ge}5$ with broken lattice translational invariance. Our computation of the magnetization and the dimerization order parameter shows the absence of the intermediate spin-liquid phase.
73 citations
TL;DR: The phase diagram of the $S = 1/2$ Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques, was presented in this article.
Abstract: We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.
64 citations
TL;DR: In a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of a state in which long-range ordered orbital currents are arranged in a staggered pattern, coexisting with a charge density wave is provided.
Abstract: We provide, for the first time, in a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of a state in which long-range ordered orbital currents are arranged in a staggered pattern, coexisting with a charge density wave. The method used is the highly accurate density-matrix renormalization group technique. This brings us closer to recent proposals that this order is realized in the enigmatic pseudogap phase of the cuprate high temperature superconductors.
52 citations
06 Nov 2003
TL;DR: In this paper, the development of update schemes for quantum lattice models simulated using world line quantum Monte Carlo algorithms is reviewed, starting from the Suzuki-Trotter mapping, and highlighting the main developments beyond Metropolis-style local updates: development of cluster algorithms, their generalization to continuous time, the worm and directedloop algorithms and finally a generalization of the flat histogram method of Wang and Landau to quantum systems.
Abstract: We review the development of update schemes for quantum lattice models simulated using world line quantum Monte Carlo algorithms. Starting from the Suzuki‐Trotter mapping we discuss limitations of local update algorithms and highlight the main developments beyond Metropolis‐style local updates: the development of cluster algorithms, their generalization to continuous time, the worm and directed‐loop algorithms and finally a generalization of the flat histogram method of Wang and Landau to quantum systems.
26 citations
4 citations
06 Nov 2003
TL;DR: In this article, a flat histogram algorithm for quantum systems is proposed, in which the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order are stochastically evaluated.
Abstract: We present generalizations of the classical flat histogram algorithm of Wang and Landau to quantum systems. The algorithms proceed by stochastically evaluating the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order. Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct calculation of the free energy and entropy.
1 citations
01 Jan 2003
TL;DR: In this article, the authors present the design and implementation details for an object-oriented C++ class library for many-body physics on finite lattices and divide the simulation in five modules which are strictly separated and interact via well defined interfaces.
Abstract: We present the design and implementation details for an object-oriented C++ class library for many-body physics on finite lattices. We divide the simulation in five modules which are strictly separated and interact via well defined interfaces. Special emphasis is put on the simulation algorithms, where we review the stochastic series expansion and the loop-operator update, both used in our Quantum-Monte-Carlo simulations. The second part of the paper is dedicated to an application from solid-state physics: the SO(5) model in two dimensions as a model for high-temperature-superconductivity. We demonstrate that this microscopic model, which aims at unifying antiferromagnetism and superconductivity, reproduces salient features of the temperature versus doping phase diagram.
01 Jan 2003
TL;DR: Numerical simulations on the quantum dimer model show that this model, originally derived as effective model for the low-energy physics of frustrated Ising models, has the right properties to be used in a physical realization of topologically protected quantum bits.
Abstract: As simulation techniques are maturing, new connection between previously separate fields appear. We present numerical simulations on the quantum dimer model. They show that this model, originally derived as effective model for the low-energy physics of frustrated Ising models, has the right properties to be used in a physical realization of topologically protected quantum bits. A topologically protected quantum bit has the advantage of being passively stable against decoherence and thus does not require error correction schemes
01 Jan 2003
TL;DR: In this article, the authors investigated the melting of the stripe phase in the square lattice hard core boson Hubbard model with nearest and next nearest neighbor repulsion using quantum Monte Carlo simulations and found that the stripe melting is realized in a first order transition at low temperatures.
Abstract: We investigate the melting of the stripe phase in the square lattice hard-core boson Hubbard model with nearest and next nearest neighbor repulsion using quantum Monte Carlo simulations. We find that the stripe melting is realized in a first order transition at low temperatures. In addition we conjecture that a nematic phase does not exist in this model