Modern techniques for solvable models

N. N. Bogolubov Jr.

This chapter is mainly a pedagogical introduction to a modern method in equilibrium finite-temperature polaron theory based on the T-product operator technique. As an example of the application of this method, Bogolubov's exactly solvable linearized polaron model, as well as Feynman's two-body oscillator model, are considered.

N. N. Bogolyubov, A. G. Shumovskaya, A. S. Shumovskiǐ

Gerald Dennis Mahan

Vieri Mastropietro

Recently, a rigorous foundation of several aspects of the theory of universality for statistical mechanics models with continuously varying exponents (among which are interacting planar Ising models, quantum spin chains, and one-dimensional Fermi systems) has been reached; it has its root in the mapping of such systems into fermionic interacting theories and uses the modern renormalization group methods developed in the context of constructive quantum field theory. No use of exact solutions is done and the analysis applies either to solvable or not solvable models. A review of such developments will be given here.

Matthew C. O'Brien, Eduardo Fradkin

Abstract The interplay between quantum and thermal fluctuations in the presence of quenched random disorder is a long-standing open theoretical problem which has been made more urgent by advances in modern experimental techniques. The fragility of charge density wave order to impurities makes this problem of particular interest in understanding a host of real materials, including the cuprate high-temperature superconductors. To address this question, we consider the quantum version of an exactly solvable classical model of two-dimensional randomly pinned incommensurate charge density waves first introduced by us in a recent work, and use the large-N technique to obtain the phase diagram and order parameter correlations. Our theory considers quantum and thermal fluctuations and disorder on equal footing by accounting for all effects non-perturbatively, which reveals a novel crossover between under-damped and over-damped dynamics of the fluctuations of the charge density wave order parameter.

D. Ya. Petrina