Higher Order Auxiliary Field Quantum Monte Carlo Methods

Bond breaking with auxiliary-field quantum Monte Carlo.

Bond stretching mimics different levels of electron correlation and provides a challenging test bed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N(2) and in the H(50) chain. To control the sign/phase problem, the phaseless AF QMC method ...

Continuous-time auxiliary field Monte Carlo for quantum impurity models

Introduction. – The development of efficient numerical methods for solving quantum impurity models has been driven in recent years by the success of dynamical mean field theory (DMFT) [1–3] and its extensions. DMFT is an approximate framework for the study of fermionic lattice models, which replaces the lattice by a quantum impurity embedded in a self-consistent bath. Both cluster-extensions of...

15 Auxiliary-Field Quantum Monte Carlo for Correlated Electron Systems

Auxiliary-field Monte Carlo for quantum spin and boson systems

We describe an algorithm for the numerical simulation of quantum spin and boson systems. The method is based on the Trotter decomposition in imaginary time and a decoupling by auxiliary Ising spins. It can be applied, in principle, to arbitrary ~random! spin systems, however, in general it suffers from the ‘‘minus-sign problem.’’ This problem is absent in the case of the Ising model in a transv...

Monte Carlo Methods for Quantum Field Theory

The intention of this paper is to review some recent and a few not-so-recent advances in Monte Carlo simulation algorithms for lattice field theory with particular regard to their applicability to full QCD computations including Ginsparg–Wilson quarks. The fundamental goals for the design of algorithms is the efficient and correct computation of quantities of physical interest; the mechanism fo...