Relationship between Hirsch-Fye and weak-coupling diagrammatic quantum Monte Carlo methods.

On the sign problem in the Hirsch–Fye algorithm for impurity problems

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further...

Diagrammatic Monte Carlo simulation of quantum impurity models – weak and strong coupling approach

Quantum Monte Carlo Algorithms for the Quantum Cluster Problem

We present a pedagogical discussion of the the Hirsch-Fye and Continuous time Quantum Monte Carlo (QMC) algorithms which may be used to study a correlated cluster embedded in an uncorrelated host, or used to solve the cluster problem in dynamical mean field theory (DMFT) or its cluster extensions. The basic algorithms are discussed, together with methods for efficient measurments and the modifi...

Diagrammatic perturbation theory and the pseudogap

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical molecular fields. We consider two types of such fields, a vector molecular field that couples to the quasiparticle spin-density and a scalar field coupled to the quasiparticle number density. The model describes quasiparticles coupled to spin or charge fluctuations, and is solved by ...

Cluster solver for dynamical mean-field theory with linear scaling in inverse temperature.

Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye ...