Susy atomic model

TL;DR

This paper introduces a simple atomic model applying supersymmetric Hubbard operators, providing exact solutions for thermodynamic properties and developing a new approximation scheme that reveals novel solutions beyond traditional slave particle methods.

Contribution

It develops an exact solution framework for a supersymmetric atomic model and introduces a new class of solutions not accessible by existing slave boson or fermion approaches.

Findings

Exact solutions for entropy and heat capacity as functions of temperature.

Identification of a new class of solutions at Q=1, N=2.

A phase diagram resembling quantum critical systems.

Abstract

We present the simplest model to which one can apply the supersymmetric Hubbard operators recently introduced. For the atomic model, $H=-E_d X_{00}$, where $X_{00} = |0><0|$ is a Hubbard operator and $E_d$ is the energy of the localized spin level, we show how one can develop exact solutions for the entropy and heat capacity as a function of temperature. With this gold standard we are able to develop a controlled approximation scheme to field theoretically treat the susy approximation at the level of mean field + gaussian corrections and test its accuracy against the widely used slave boson and slave fermion approximations. We find that in addition to slave boson and slave fermion solutions, a new class of solutions exists in the physical case Q = 1, N = 2 which can be properly treated by neither previously existing approach. The phase diagram generated by the mean field saddle-point bears a superficial resemblance to the V-shaped phase diagram common to systems close to a quantum critical point and may provide a natural starting point for investigations of strongly correlated models capturing this physics.