 96226 Datta N., Fern\'andez R., Froehlich J., ReyBellet L.
 Lowtemperature phase diagrams of quantum lattice systems. II. Convergent
perturbation expansions and stability in systems with infinite degeneracy.
(208K, LaTeX)
May 22, 96

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We study groundstates and lowtemperature phases of quantum lattice systems in
statistical mechanics: quantum spin systems and fermionic or bosonic lattice gases.
The Hamiltonians of such systems have the form
$$
H\,=\,H_0\,+\,tV,
$$
where $H_0$ is a classical Hamiltonian, $V$ is a quantum perturbation, and $t$
is the perturbation parameter. Conventional methods to study such systems
cannot be used when $H_0$ has infinitely many groundstates. We construct a
unitary conjugation transforming $H$ to a form that enables us to find its
lowenergy spectrum (to some finite order $>1$ in $t$) and to understand how
the perturbation $tV$ lifts the degeneracy of the groundstate energy of
$H_0$. The purpose of the unitary conjugation is to cast $H$ in a form that
enables us to determine the lowtemperature phase diagram of the system. Our
main tools are a generalization of a form of RayleighRitz analytic
perturbation theory analogous to Nekhoroshev's form of classical perturbation
theory and an extension of PirogovSinai theory.
 Files:
96226.tex