Auxiliary-field Monte Carlo for quantum spin and boson systems
نویسندگان
چکیده
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 transverse field in arbitrary dimensions and geometries. We show test results for the spin-1/2 XY model, the one-dimensional transverse Ising model with disorder, and the phase transition induced by a transverse field in the two-dimensional Ising model.
منابع مشابه
Neutron matter at zero temperature with an auxiliary field diffusion Monte Carlo method
The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo method for the spatial degrees of freedom and auxiliary field Monte Carlo method to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many-nucleon systems (...
متن کاملComputational Studies of Strongly Interacting Ultracold Atoms
We develop and apply computational methods to investigate correlation effects in atomic and molecular systems, and in optical lattice systems. Problems from both classes are studied synergistically. We quantified effects of many-body correlations in trapped atomic Bose gases; developed auxiliary-field quantum Monte Carlo method for Bosons and fermions whose computational cost scales as N^3-N^4 ...
متن کاملComputational Studies of Strongly Interacting Ultracold Atoms - - Final Report
We develop and apply computational methods to investigate correlation effects in atomic and molecular systems, and in optical lattice systems. Problems from both classes are studied synergistically. We quantified effects of many-body correlations in trapped atomic Bose gases; developed auxiliary-field quantum Monte Carlo method for Bosons and fermions whose computational cost scales as N^3-N^4 ...
متن کاملQuantum phase transition and correlations in the multi-spin-boson model
We consider multiple noninteracting quantum mechanical two-level systems coupled to a common bosonic bath and study its quantum phase transition with Monte Carlo simulations using a continuous imaginary time cluster algorithm. The common bath induces an effective ferromagnetic interaction between the otherwise independent two-level systems, which can be quantified by an effective interaction st...
متن کامل