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Summary
The paper presents a phase-space approach to constructing lattice models for complex physical systems, bypassing obstructions in identifying appropriate states that transform between momentum and real space while retaining correlation, entanglement, and geometric properties.
Highlights
- Introduces a phase-space approach to lattice models, embedding real space within a Bloch vector space at each momentum.
- Discusses the construction of Wannier states and their projection onto real space, considering quantum statistics, Hamiltonian-induced interactions, and geometric effects.
- Applies the framework to study mean-field superconductivity and spin-fluctuation-mediated unconventional pairing symmetries.
- Analyzes a single flat-band case on a 2D square octagon lattice, showcasing the framework's effectiveness in analytically solving unconventional pairing symmetries.
- Finds that while superconductivity exhibits global coherence in momentum space, the pairing symmetry is dictated by compact orbitals aligned with their reps of the underlying lattice symmetry.
- Applies the method to the SO material Lu2Fe3Si5, finding the coexistence of uniform s-wave pairing across two bands and nodal s-wave symmetry for a third band.
Key Insights
- The phase-space approach offers a robust, obstruction-free lattice model for complex many-body systems and their exotic excitations, providing a flexible framework for studying various phenomena, including superconductivity and spin liquids.
- By working within momentum space and embedding real space within the Bloch vector space at each momentum, the approach inherently fixes the localization and uncertainty of states in real and momentum space.
- The method allows for the inclusion of quantum statistics and braiding phases as variational parameters, enabling the modeling of fractional quantum Hall or fractional Chern states by attaching vortices in Bloch vector space to orbital states.
- The approach can stabilize liquid states of compact orbitals in flat-band degenerate manifolds or spin-singlet liquids in quantum spin-liquid metals, offering new possibilities for exploring exotic many-body states.
- The framework's application to superconductivity in SO materials reveals the importance of compact orbitals in determining pairing symmetry, highlighting the interplay between lattice symmetry and superconducting properties.
- The coexistence of multiple pairing symmetries, as observed in Lu2Fe3Si5, suggests the potential for complex multiband superconductivity, which can be further explored using the phase-space approach.
- The method's flexibility and ability to incorporate various interactions and effects make it a valuable tool for investigating a wide range of phenomena in condensed matter physics.
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Citation
Sharma, R. O., & Das, T. (2024). Phase-Space Approach to Wannier Pairing and Bogoliubov Orbitals in Square-Octagon Lattices (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20054