A new fixed point for Mottness

Understanding electronic behavior in solids remains a central challenge in condensed matter physics. Historically, Landau's Fermi liquid theory, BCS superconductor theory, and Bloch’s electron band theory have provided robust frameworks for describing electronic states in conventional metals, superconductors, insulators, and semiconductors. However, these frameworks fail to fully account for the physics observed in strongly correlated electron systems, notably Mott insulators and their doped counterparts, which exhibit unconventional superconductivity and novel topological phases. In this thesis, we propose a novel universality class, characterized by zeros in the single-particle Green function, exemplified explicitly by the Hatsugai-Kohmoto (HK) model. This approach introduces a new quartic fixed point that captures essential physics beyond traditional Fermi liquid theory. The thesis is organized in 6 chapters. In the introductory chapter, we briefly review the basic features of Landau's Fermi liquid theory, BCS superconductor theory, and Bloch’s electron band theory on topological insulators as well as some experimental evidence that deviates from the traditional understandings. Chapter 2 establishes the stability of the HK model by demonstrating its robustness under perturbations from local interactions. The HK model is shown to naturally accommodate spectral weight bifurcation characteristic of Mott physics, with its sole instability arising via a superconducting channel consistent with previous theoretical insights. Chapter 3 extends this analysis to compute superconducting properties from the solvable HK model. Our findings reveal critical deviations from conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity, such as a first-order superconducting transition, the emergence of a tricritical point, and significant modifications in thermodynamic and electronic properties arising from strong correlations, termed Mottness. Chapters 4 and 5 revisit the topological invariants and foundational Luttinger's theorem and explore their limitations within non-Fermi liquid systems. In Chapter 4, the discrepancy between the topological invariant and the Hall conductance is addressed by an exact model. By proposing a generalized Luttinger count incorporating topological terms, I introduce in Chapter 5 that the failure of Luttinger's theorem is linked to generalized 't Hooft anomaly associated with zeros of the Green function. This analysis offers deeper insights into the interplay between topology and strong correlations. Chapter 6 introduces the orbital Hatsugai-Kohmoto (OHK) model, systematically bridging the gap between the exactly solvable HK model and the extensively studied Hubbard model. The OHK model efficiently captures rich Mott physics with remarkable computational efficiency, providing accurate reproductions of essential properties of strongly correlated materials, including dynamical spectral weight transfer and antiferromagnetic correlations. Overall, this thesis establishes a robust theoretical foundation for understanding the rich physics of strongly correlated electron systems, extending the scope of conventional band and Fermi liquid theories.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Zhao, Jinchao

Contributors dc:contributor

• Phillips, Philip W.
• Bradlyn, Barry
• Madhavan, Vidya
• Yunes, Nicolas

• Condensed Matter Physics
• Strongly Correlated Electrons
• Mott Physics

Statement dc:rights

• Copyright 2025 Jinchao Zhao

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129906

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129906