Fermionic quantum spin glass transitions

Abstract

This article reviews recent progress of the analytical theory of quantum spin glasses (QSG). Exact results for infinite range and one loop renormalisation group calculations for finite range models of either insulating or metallic type are presented. We describe characteristics of fermionic spin glass transitions and of fermionic correlations which are affected by these transitions and by spin glass order. Connections between tricritical thermal-and T = 0 QSG transitions are described. A general phase diagram with tricritical QSG transitions caused either by random chemical potential or by elastic electron scattering, and implying discontinuous T = 0-transitions in weak and in strong filling regimes, is also derived.

Fermionic Thouless-Anderson-Palmer equations

“…This is exactly the equation found in [6,9,14] for q with a replicated quantum-field-theory approach.…”

“…It is believed [2,15] that the complete set of solutions to the TAP equations is equivalent to the fully replica-symmetry-broken solution in the quantum-field theory [6][7][8][9], so far only known for half-filling. We were able to solve the fermionic TAP equations numerically on the T = 0 axis and to determine the first-order transition at µ c ≈ 0.8 where the paramagnetic and spin-glass free energies become equal.…”