Non-orthogonal multi-Slater determinant expansions in auxiliary field quantum Monte Carlo

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...

A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations.

We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N(2)) computations, where N is the system size. ...