Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$

TL;DR

This paper reviews recent advances in quantum geometry, including its generalizations and applications to $X$-wave magnets, revealing universal physics in transport and optical phenomena with new analytical insights.

Contribution

It introduces generalized quantum geometry frameworks and applies them to $X$-wave magnets, deriving analytical formulas for various physical responses.

Findings

Universal physics in $X$-wave magnets for Hall effects and magneto-resistance

Analytical formulas for optical and magnetic responses in two-band models

Quantum Fisher information as a quantum metric in density matrix geometry

Abstract

Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the spin degrees of freedom. It is related to electromagnetic cross responses. Quantum geometry is generalized to non-Hermitian systems and density matrices. Especially, the latter is quantum information geometry, where the quantum Fisher information naturally arises as quantum metric. We apply these results to the $X$-wave magnets, which include $d$% -wave, $g$-wave and $i$-wave altermagnets as well as $p$-wave and $f$-wave magnets. They have universal physics for anomalous Hall conductivity, tunneling magneto-resistance and planar Hall effect. We also study magneto-optical conductivity, magnetic circular dichroism and Friedel oscillations in the $X$-wave magnets. Various analytic formulas are derived in the case of two-band Hamiltonians. This paper presents a review of recent progress together with some original results.