Fermionic Ising glasses with BCS pairing interaction in the presence of a transverse field

TL;DR

This paper investigates a fermionic Ising spin glass model with BCS pairing under a transverse field, revealing phase transitions and the suppression of pairing with increasing quantum fluctuations.

Contribution

It introduces a combined model of fermionic spin glasses with BCS pairing in a transverse field and analyzes its phase diagram using path integral formalism.

Findings

Transition temperature decreases with transverse field for small pairing strength.

A local pairing (PAIR) phase exists and is suppressed by the transverse field.

Quantum critical point occurs where the transition line ends.

Abstract

In the present work we have analyzed a fermionic infinite-ranged Ising spin glass with a local BCS coupling in the presence of transverse field. This model has been obtained by tracing out the conduction electrons degrees of freedom in a superconducting alloy. The transverse field \Gamma is applied in the resulting effective model. The problem is formulated in the path integral formalism where the spins operators are represented by bilinear combination of Grassmann fields. The problem can be solved by combining previous approaches used to study a fermionic Heisenberg spin glass and a Ising spin glass in a transverse field. The results are show in a phase diagram T/J {\it versus} \Gamma/J (J is the standard deviation of the random coupling J_{ij}) for several values of g (the strength of the pairing interaction). For small g, the line transition T_c(\Gamma) between the normal paramagnetic phase and the spin glass phase decreases when increases \Gamma, until it reaches a quantum critical point. For increasing g, a PAIR phase (where there is formation of local pairs) has been found which disappears when is close to \Gamma_c showing that the transverse field tends to inhibited the PAIR phase.