Datta N., Fernandez R., Froehlich J.
Low-temperature phase diagrams of quantum lattice systems. I.
Stability for quantum perturbations of classical systems with
finitely-many ground states
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ABSTRACT. Starting from classical lattice systems in $d\ge 2$ dimensions
with a regular zero-temperature phase diagram, involving a finite
number of periodic ground states, we prove that the addition of a
small quantum perturbation and/or increasing the temperature produce
only smooth deformations of their phase diagrams. The quantum
perturbations can involve bosons or fermions and can be of infinite
range but decaying exponentially fast with the size of the bonds.
For fermions, the interactions must be given by monomials of
even degree in creation and annihilation operators.
Our methods can be applied to some anyonic systems as
well. Our analysis is based on an extension of Pirogov-Sinai theory to
contour expansions in $d+1$ dimensions obtained by iteration of the
Duhamel formula.