Ansgar Dorneich

Finite-temperature phase diagram of hard-core bosons in two dimensions.

We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.

Quantum phase transitions in the two-dimensional hardcore boson model

We use two quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near (V 1 ) and next near (V 2 ) neighbor repulsion. At half filling we find three phases: superfluid (SF), checkerboard solid, and striped solid depending on the relative values of V 1 ,V 2 , and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases coexist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: coexistence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the V 2 interaction.

Analytical and numerical study of hardcore bosons in two dimensions

We study various properties of bosons in two dimensions interacting only via on-site hardcore repulsion. In particular, we use the lattice spin-wave approximation to calculate the ground-state energy, the density, the condensate density, and the superfluid density in terms of the chemical potential. We also calculate the excitation spectrum, \ensuremath{\omega}(k). In addition, we perform high precision numerical simulations using the stochastic series expansion algorithm. We find that the spin-wave results describe extremely well the numerical results over the whole density range 0\ensuremath{\leqslant}\ensuremath{\rho}\ensuremath{\leqslant}1. We also compare the lattice spin-wave results with continuum results obtained by summing the ladder diagrams at low density. We find that for \ensuremath{\rho}\ensuremath{\leqslant}0.1 there is good agreement, and that the difference between the two methods vanishes as

Phasediagram and Scaling Properties of the Projected SO(5) Model in Three Dimensions

{\ensuremath{\rho}}^{2}

Object-Oriented C++ Class Library for Many Body Physics on Finite Lattices and a First Application to High-Temperature Superconductivity

for

Destruction of Superfluid and Long Range Order by Impurities in Two Dimensional Systems

\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\rho}}}

SO(5) symmetry in t-J and hubbard models

0. This offers the possibility of obtaining precise continuum results by taking the continuum limit of the spin-wave results for all densities. Finally, we study the finite-temperature phase transition numerically for the entire density range, and compare with low density predictions.

SO(5) theory of high-Tc superconductivity: models and experiments

We study the scaling properties of the quantum projected SO(5) model in three dimensions by means of a highly accurate Quantum-Monte-Carlo analysis. Within the parameter regime studied (temperature and system size), we show that the scaling behavior is consistent with a SO(5)-symmetric critical behavior in the numerically accessible region. This holds both when the symmetry breaking is caused by quantum fluctuations only as well as when also the static (mean-field) symmetry is moderately broken. We argue that possible departure away from the SO(5) - symmetric scaling occurs only in an extremely narrow parameter regime, which is inaccessible both experimentally and numerically.

Accessing the dynamics of large many-particle systems using the stochastic series expansion.

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.

Strong-coupling theory for the Hubbard model

We use the stochastic series expansion (SSE) Quantum Monte Carlo algorithm to examine the effect of impurities, in the form of disordered chemical potential, on the phase diagram of the hardcore bosonic Hubbard model in two dimensions. This model is often used to study the properties of several physical systems such as Helium adsorbed on surfaces and granular superconductors. We show that in two dimensions, no matter how weak the disorder is, it will always destroy the long range density wave order (checkerboard solid) present at half filling and strong near neighbor (nn) repulsion. In addition part of the superfluid phase surrounding the checkerboard solid is also destroyed. We study properties of the glassy phase thus generated at strong nn coupling, and the possibility of other localized phases at weak nn repulsion, i.e. Anderson localization. The SSE algorithm is used to measure several physical quantities such as the superfluid density, energy gaps, equal and unequal time Green functions.