Emergent gauge fields and their nonperturbative effects in correlated electrons

TL;DR

This paper reviews how topological excitations like skyrmions and monopoles influence the nonperturbative behavior of correlated electrons, bridging real-space and momentum-space perspectives in condensed matter physics.

Contribution

It introduces a framework incorporating topologically nontrivial excitations into the description of correlated electrons, reconciling competing theoretical approaches.

Findings

Topological excitations significantly affect electron dynamics.

Nonperturbative effects reveal new physical phenomena.

Bridging real-space and momentum-space descriptions enhances understanding.

Abstract

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner's and Anderson's physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high T$_{c}$ superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner's description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner's paradigm. In this review article we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. ......