โ Scribed by S Leibler; H Orland
No coin nor oath required. For personal study only.
The partition function of quantum spin systems is represented by a functional integral over "time"-dependent magnetic fields. It is evaluated in the saddle-point approximation. In this way, the excitations of the system are derived from first principles, and their interactions are obtained.
The thermodynamics of quantum spin systems given by a Hamiltonian where S, , S, are quantum spin operators on the sites i andj, has already become a classical subject of studies. It is difficult even to mention all the methods used in this field, but one can group them into two general classes which are not of course mutually exclusive.
In the first group of methods one tries to describe approximately the quantum spin system by a set of bosons. After such bosonisation one uses another approximation technique such as some kind of variational principle. This is the case in many works, from the early ones of Holstein andprimakoff [1] and Bloch [2], to the recent papers of Goldhirsch PI al. 131.
The second class of methods consists of all perturbation techniques. We include here both the procedures in which one explicitly makes some perturbation expansion and those which are in fact equivalent. Thus one finds in this class the so-called Green function method [4], Matsubara's diagram technique [5], low [6] or high-temperature [7] expansions and many others.
All these methods give in fact a very good description of the thermodynamics of the system. Thanks to them one can understand the behaviour of many physical ferro-or antiferromagnets. The only drawback of these methods is a non-systematic character of approximations. One can hardly control the bosonisation process and/or the following approximation techniques, the Green function decouplings or resumming of diagrams.
In this paper we present a new way of studying the thermodynamics of quantum spin systems. This is a functional integral method, in which one writes the partition function Z as a path integral and then employs usual field theoretical functional procedures. This is a generalization for the quantum case of the functional methods used for classical spin systems [S]. 277
๐ SIMILAR VOLUMES
A review of the basic strategies that we have developed for the simulation of dynamic correlation functions in quantum systems is provided. Three methods are considered: (a) the analytic continuation of imaginary (thermal) time correlation functions to real times; (b) direct evaluation of thermally
Practical, structure-preserving methods for integrating classical Heisenberg spin systems are discussed. Two new integrators are els. This article addresses issues of practicality and derived and compared, including (1) a symmetric energy and spinefficiency in the numerical solution of a conservativ