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The meron-cluster algorithm was previously used to extensively study the physics associated with the spontaneous breaking of a discrete symmetry. We recently discovered that a larger class of models with spontaneous breaking of continuous…
The recent solution to the fermion sign problem allows, for the first time, the use of cluster algorithm techniques to compute certain fermionic path integrals. To illustrate the underlying ideas behind the progress, a cluster algorithm is…
A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous…
Recent research shows that the partition function for a class of models involving fermions can be written as a statistical mechanics of clusters with positive definite weights. This new representation of the model allows one to construct…
A cluster algorithm is constructed and applied to study the chiral limit of the strongly coupled lattice Schwinger model involving staggered fermions. The algorithm is based on a novel loop representation of the model. Finite size scaling…
We study a strongly correlated fermionic model with attractive interactions in the presence of disorder in two spatial dimensions. Our model has been designed so that it can be solved using the recently discovered meron-cluster approach.…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
$SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions are considered at high quark chemical potential $\mu$ and any temperature $T$. In the strong coupling regime (sufficiently small $\beta$) they have been…
Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we…
Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute…
Typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on cluster algorithms which do not involve the determinant and involve a more physically relevant sampling of the configuration…
The triangular-lattice Fermi-Hubbard model has been extensively investigated in the literature due to its connection to chiral spin states and unconventional superconductivity. Previous simulations of the ground state of the doped system…
The partition function of two dimensional massless staggered fermions interacting with U(N) gauge fields is rewritten in terms of loop variables in the strong coupling limit. We use this representation of the theory to devise a non-local…
Single- and multi-band Hubbard models have been found to describe many of the complex phenomena that are observed in the cuprate and iron-based high-temperature superconductors. Simulations of these models therefore provide an ideal…
Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems.…
Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip…
We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the na\"ive $U(2)$ symmetry is…
We study two-color lattice QCD with massless staggered fermions in the strong coupling limit using a new and efficient cluster algorithm. We focus on the phase diagram of the model as a function of temperature $T$ and baryon chemical…
We examine a (3+1)-dimensional model of staggered lattice fermions with a four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian formulation. This model cannot be simulated with standard fermion algorithms because those…
The recently developed Meron-Cluster algorithm completely solves the exponentially difficult sign problem for a number of models previously inaccessible to numerical simulation. We use this algorithm in a high-precision study of a model of…