The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

TL;DR

This paper introduces a new method to analyze the phase diagram of the finite temperature Mott transition in the Hubbard model, revealing the critical point as a cusp catastrophe and elucidating the bifurcation structure of the transition.

Contribution

A novel approach for calculating the DMFT fixpoint surface that overcomes convergence issues and applies dynamical systems theory to characterize the transition's critical properties.

Findings

The critical point is a cusp catastrophe in parameter space.

Hysteresis boundaries are saddle-node bifurcations.

The critical end point relates to a critical eigenmode of the Jacobian.

Abstract

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.