Geometrical properties of the ground state manifold in the spin boson model

TL;DR

This paper investigates how a quantum dissipative environment influences the geometrical and topological properties of the ground state manifold in a spin-1/2 system, revealing a universal metric singularity at quantum phase transitions.

Contribution

It introduces an analysis of the geometrical properties of the ground state manifold in the spin boson model, highlighting the role of metric singularities in quantum phase transitions.

Findings

Quantum phase transition linked to metric singularity and diverging spin susceptibility.

Absence of transition at finite temperature results in smooth metric variation.

Universal behavior of the metric near zero-temperature quantum critical points.

Abstract

Geometrical and topological properties of quantum ground state manifolds permits to characterize phases of matter, and identify phase transitions. Here, we study the effect of a quantum dissipative environment on the geometrical properties of the ground state manifold of a single spin 1/2 in an external effective magnetic field. We show that the quantum phase transition at zero temperature in the model is associated with a universal metric singularity related to the divergence of the spin susceptibility. The absence of transition at finite temperature corresponds to a smooth variation of the associated metric with temperature, without singular points.