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Many condensed-matter and open quantum systems are far too complex to handle with standard low‑energy models. Conventional approaches such as field theory, tight-binding models, or reduced density-matrix methods often neglect high-energy states in a simplified manner, thereby missing many important aspects of physics. In this talk, I will first review modern geometric approaches, including quantum metric, gauge theory, and symmetry representations, that provide new tools for addressing these challenges. I will then present our phase-space orbital framework, in which lattice hopping is mediated by effective gauge fields arising from high-energy super-exchanges. I illustrate this via Majorana orbitals in the Kitaev model, Ising/Rashba pairings in 2D IrTe2, and altermagnetism in 2D RuO2. Finally, I discuss extending these geometric ideas to open quantum systems via gauge-field bath modeling and the future role of AI in advancing low-energy theory.
References
1. K.B Yogendra, G Baskaran, T Das, PRX 15, 031020 (2025).
2. R.O. Sharma, T. Das, PRB 111, 214522 (2025).
3. K. Dutta, Rajesh O. Sharma, S. Das, I. Dasgupta, T. Das, T. Saha-Dasgupta, arXiv:2602.16228
4. Gurpreet Singh, R. O. Sharma, T. Das, manuscript in preparation. |