Quantum Phase Transitions induced by Infinite Dilution in the Fock Space: a General Mechanism. Proof and discussion

TL;DR

This paper demonstrates a general mechanism for first-order quantum phase transitions in lattice systems caused by infinite dilution of low-energy states, with a derived critical point condition and comparisons to solvable models.

Contribution

It introduces a universal mechanism for quantum phase transitions driven by state dilution, extending understanding beyond specific models.

Findings

First-order quantum phase transition occurs when cavity and reservoir energies are equal.

Derived a general equation for the critical point in such transitions.

Compared theoretical results with exactly solvable models like the Quantum Rem model.

Abstract

We prove that lattice quantum systems may undergo a first-order quantum phase transition through a general mechanism which consists in an infinite dilution of the states associated to (or, more in general, near to) the lowest energy levels. The equation giving the critical point is derived and discussed at several degrees of generalizations: given an infinitesimal portion of the Fock space, i.e., the cavity space, and its complement, i.e., the reservoir space, in the thermodynamic limit, a first-order quantum phase transition takes place when the cavity and reservoir energies are equal. A comparison with some particular exact solvable cases as, e.g., the Quantum Rem model, is made.