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Generalized Peierls Substitution for Wannier Obstructions: Response to Disorder and Interactions.

Shuai A Chen¹, Roderich Moessner¹, Tai Kai Ng²

¹Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany.

Physical Review Letters

|September 26, 2025

Summary

This study introduces a new framework to describe complex band systems, improving predictions for electromagnetic responses in materials with nontrivial quantum geometry and interactions. It addresses challenges posed by Wannier obstructions in condensed matter physics.

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Area of Science:

Condensed matter physics
Quantum geometry
Materials science

Background:

Complex band systems with Wannier obstructions challenge traditional descriptions using atomic orbitals.
Predicting electromagnetic responses in these systems is difficult, especially with disorder and interactions.

Purpose of the Study:

To develop a generalized framework for describing complex band systems with Wannier obstructions.
To effectively incorporate interactions and disorder in the presence of nontrivial quantum geometry.

Main Methods:

Introduced a generalized Peierls substitution framework using Lagrange multipliers.
Enforced constraints of Wannier obstructions within the band of interest.
Obtained effective descriptions for interactions and disorder.

Main Results:

Developed a method to handle Wannier obstructions in band structure calculations.
Enabled effective descriptions of quantum geometric effects alongside interactions and disorder.
Successfully applied the framework to diamagnetic response in superconductors and delocalization in metals.

Conclusions:

The generalized Peierls substitution framework provides a robust method for studying complex band systems.
This approach enhances the understanding of electromagnetic responses and material properties influenced by quantum geometry, interactions, and disorder.