Correlation Effects and Quantum Geometry in Adiabatic Spin Dynamics

• Applicant: Professor Dr. Michael Potthoff
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 449872909

This project explores novel physics at the intersection of topologically nontrivial electronic structure, quantum geometry, electron correlations, and slow real-time dynamics in condensed-matter systems. We consider systems with local magnetic moments (LMMs) exchange-coupled to various lattice-electron models. The state of the LMMs is represented by a point in the space of classical spin configurations ("S-space"), the dynamical, topological and geometrical properties of which will be studied in detail. In addition this provides us with new perspectives on the nonlocal magnetic response of prototypical models for QUAST materials: flat-band systems (studied experimentally in P5), transition-metal dichalcogenides (P6), or Weyl-Kondo semimetals (P1), along with disordered and correlated Chern insulators (with P4) and topological Mott insulators (with P5). More specifically, we will extend the adiabatic spin-dynamics theory by combining nonlinear response theory in the local exchange coupling J and an expansion in the retardation time, quantifying deviations from the adiabatic limit. This allows us to access shorter time scales, as addressed in P6, and provides a "geometrization'" of close-to-adiabatic spin dynamics, where the geometric spin torque, spin friction and quantum metric are seen as aspects of the quantum-geometrical tensor (QGT) on S-space. In addition, novel geometrical interactions from terms quadratic in time derivatives of the spins find their interpretation in the geodesics equation. New ways to topologically characterize correlated electron systems with LMMs are explored in cooperation with P4. Here, we focus on the impact of electron correlations on the topological structure of S-space, characterized by spin-Chern numbers, and deduce the implications of local S-space topology on the correlated electronic structure of gapped systems, including (k-space) Z and Z2 topological and disordered systems. With P4 and P5, we will apply this dual, S- and k-space topological characterization to Mott and Anderson insulators. Systems with a few quantum-spin impurities coupled to Z and Z2 insulators or BCS superconductors will be studied with quantum-chemistry methods from P7 to find remnants of a finite spin-Chern number in the quantum-spin case and thereby to characterize the J-spectral flow of one-particle Green’s function poles and zeros, and of the two-particle excitations. Electron correlations will significantly impact the quantum geometry of S-space. This offers the exciting perspective of correlation-driven singularities in the geometry and related feedback on the electronic structure. Together with P4, P1, we aim for methodical extensions of TPSC, D-TRILEX and DGA approaches to compute the QGT and derived differential-geometrical quantities for gapped correlated systems.

• DFG Programme: Research Units
• Subproject of: FOR 5249: Quantitative Spatio-Temporal Model-Building for Correlated Electronic Matter
• Co-Investigator: Professor Dr. Alexander Lichtenstein