This dissertation delves into the exploration of novel transport phenomena in quantum matter, with a particular emphasis on the strange metal problem and the thermal Hall effect, both of which have been observed in cuprate high-temperature superconductors. Regarding the strange metal problem, we begin by investigating a series of lattice models constructed from the Sachdev-Ye-Kitaev (SYK) models, which provide a robust mechanism for the strange metal phenomenology. Furthermore, we apply insights from the SYK model to the critical Fermi surface problem to construct a strange metal with a well-defined Fermi surface. The research ultimately leads to a controlled large $N$ theory that explains the behavior of the strange metal in a comprehensive manner. In regards to the thermal Hall effect, this dissertation explores various potential heat carriers and heat conduction mechanisms. Firstly, we investigate the scenario where the Hall effect arises due to the Berry curvature of emergent excitations. Secondly, we consider situations in which thermal Hall effect is produced by phonons through the skew-scattering mechanism or the side-jump mechanism.
This dissertation delves into the exploration of novel transport phenomena in quantum matter, with a particular emphasis on the strange metal problem and the thermal Hall effect, both of which have been observed in cuprate high-temperature superconductors. Regarding the strange metal problem, we begin by investigating a series of lattice models constructed from the Sachdev-Ye-Kitaev (SYK) models, which provide a robust mechanism for the strange metal phenomenology. Furthermore, we apply insights from the SYK model to the critical Fermi surface problem to construct a strange metal with a well-defined Fermi surface. The research ultimately leads to a controlled large N theory that explains the behavior of the strange metal in a comprehensive manner. In regards to the thermal Hall effect, this dissertation explores various potential heat carriers and heat conduction mechanisms. Firstly, we investigate the scenario where the Hall effect arises due to the Berry curvature of emergent excitations. Secondly, we consider situations in which thermal Hall effect is produced by phonons through the skew-scattering mechanism or the side-jump mechanism.
The discovery of high-temperature superconductors has raises questions that extend beyond the scope of quasiparticles, a foundational concept in condensed matter theory. This dissertation explores new theoretical approaches to quantum matter without quasiparticle excitations, with a particular focus on quantum criticality and the associated superconductivity in correlated electron compounds. The soluble Sachdev-Ye-Kitaev (SYK) model has recently emerged as a fascinating platform to address the unusual metallic states with T-linear resistivity. We first consider differ- ent variants of random Hubbard models, which share many similarities to key aspects of the original SYK model. Using a large M analysis and a renormalization group method, we propose the existence of quantum critical points with fractionalized excitations separating two distinct phases, which provides insights into the quantum phase transitions and non-Fermi liquid behaviors observed in cuprate superconductors. In the second part of this dissertation, we examine the interplay between non-Fermi liquids and superconductivity with two different pairing mechanisms. Under the framework of random Hubbard model, we demonstrate that superconductivity emerging from non-Fermi liquids strongly deviates from the BCS theory by tuning the relative strength of hopping and exchange interactions. Furthermore, we investigate a two-dimensional Yukawa-SYK model with spatially randomn interactions coupling a Fermi surface to a scalar field associated with a quantum phase transition. Our theory agrees well with transport properties analysed in cuprates, such as a T-linear resistivity and Planckian dissipation.
This dissertation is a study of various aspects of metals with strong interactions between electrons, with a particular emphasis on the problem of charge transport through them. We consider the physics of clean or weakly-disordered metals near some quantum critical points, and highlight novel transport regimes that could be relevant to experiments. We then develop a variety of exactly-solvable lattice models of strongly interacting non-Fermi liquid metals using novel non-perturbative techniques based on the Sachdev-Ye-Kitaev models, and relate their physics to that of the ubiquitous “strange metal” normal state of most correlated-electron superconductors, providing controlled theoretical insight into the possible mechanisms behind it. Finally, we use ideas from the field of quantum chaos to study mathematical quantities that can provide evidence for the existence of quasiparticles (or the lack thereof) in quantum many-body systems, in the context of metals with correlated electrons.
Essentially all high temperature superconductors display a ``strange metal'' regime above their critical temperatures, where electrical and thermal transport cannot be explained within the traditional Fermi liquid paradigm of quasiparticle excitations. This paper focuses on the first, and newly discovered, solvable theory of a disordered metal without quasiparticle excitations, obtained by extending the Sachdev-Ye-Kitaev (SYK) models to finite spatial dimensions. The complete thermoelectric conductivity matrix is computed, and a surprising exact relation is found between the Seebeck coefficient and the derivative of the thermodynamic entropy with respect to the density. These computations are then compared with holographic theories which map strange metals onto black holes in theories of quantum gravity with one extra spatial dimension.
This dissertation presents a comprehensive investigation of fermionic quantum matter into the intricate relationship between quantum chaos, thermalization, and their connection to gravitational duals, with particular emphasis on the Sachdev-Ye-Kitaev (SYK) model and its extensions. Through an integrated approach combining analytical solutions in the large-N limit with advanced numerical techniques, we explore fundamental questions in quantum many-body physics, including the interplay of chaos and ergodicity, universal transport in non-Fermi liquids, and the role of gravitational analogs in strongly correlated systems. We first demonstrate that coupled SYK lattices evade instantaneous thermalization despite weak charge fluctuations, governed by a discrete wave equation dependent solely on hopping strength, independent of on-site interactions. Thermodynamically, coupled SYK models exhibit critical exponents universal to van der Waals fluids and AdS black holes, yet diverge from the Hawking-Page transition at ultralow temperatures, revealing a continuum of first-order phase transitions. They simultaneously retain the quantum chaotic properties of both a single-dot SYK model and black holes. In extended SYK chains, we identify a universal DC conductivity bound across interaction regimes, identifying crossovers between insulating, Fermi liquid, strange metal, and bad metal phases with signatures of holographic insulator behavior. Quench dynamics in mixed SYK systems reveal rapid thermalization without prethermal plateaus, enabling direct observation of thermalization in closed quantum systems in the thermodynamic limit. To diagnose ergodicity-breaking, we introduce the Krylov variance, a probe of operator localization in Krylov space, validated through mass-deformed SYK and quantum East models. Finally, we uncover Page curve entanglement dynamics and temporal quantum phase transitions in entanglement Hamiltonians of interacting fermionic chains, where symmetry-sector crossings highlight limitations of perturbative calculations performed around initial times, such as in Hawking’s analysis of black hole evaporation. We provide a condensed matter analog of the holographic “island formula” — a mechanism invoking quantum extremal surfaces to resolve the black hole information paradox. Methodologically, this work integrates large-N-type expansions, Keldysh contour techniques, and numerical methods to bridge condensed matter physics, quantum information, and gravitational duality. The results establish SYK-type systems as a universal framework for studying non-Fermi liquids, quantum criticality, and black hole analogs, while paving the way for exploring bosonic extensions and generalizations to open quantum systems.
This dissertation investigates the role of disorder in quantum many-body systems, focusing on strange metals and spin glass systems. For strange metals, we analyze the low-frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at arbitrary densities, combining analytical and numerical methods. Building on these insights, we study the overdoped random t-J model, demonstrating that strange metal behavior persists across the entire doping range. We also show that the critical metal develops an instability to a low-doping spin-glass phase, and compute the critical doping value. Furthermore, we explore the chaotic properties of a distinct strange metal model—the large N theory of a critical Fermi surface—and establish that it exhibits maximal quantum chaos. For spin glass systems, we examine the low-energy spectrum and Parisi replica-symmetry-breaking function in the quantum Ising model with infinite-range random exchange interactions with the presence of transverse and longitudinal fields. In the spin glass phase, we find that the local spin spectra are gapless and provide a detailed analysis of the phase diagram. Additionally, we investigate the quantum spherical p-rotor model in an external field, showing that the spin glass phase remains robust across a wide range of field strengths. The potential experimental applications of these findings are also discussed.
In this dissertation, which is situated in the field of theoretical condensed matter physics, we investigate many-body effects in altermagnets and electron–phonon systems. Specifically, we study a Heisenberg model for two-dimensional altermagnets, a dissipative variant of the Yukawa–Sachdev–Ye–Kitaev (YSYK) model, and the Holstein model. In all of these systems, the presence or absence of quasiparticles plays a central role. Consequently, the description of these quasiparticles and their influence on the state of the system constitute the primary focus of this work. Since the Heisenberg model can be bosonized using the Holstein–Primakoff transformation, all systems considered in this dissertation can be analyzed using many-body methods, in particular within the framework of Green's function techniques. Altermagnets constitute a recently identified class of magnetic materials characterized by their distinct symmetry properties. They combine properties of both ferromagnets and antiferromagnets, thereby offering promising opportunities for future applications, for example in spintronics. Consequently, they have become the subject of intense current research, and new candidate altermagnetic materials are continuously being proposed. The central question addressed in this part of the dissertation is, using nonlinear spin-wave theory, whether the collective magnetic excitations, namely magnons, are stable at zero temperature or undergo spontaneous decay driven exclusively by quantum-mechanical effects. The dissipative YSYK model belongs to the class of SYK models, which describe strongly coupled chaotic systems with Gaussian-distributed interactions. In the limit of an infinite number of particles, these models can be solved exactly at the level of the self-energy. They do not possess quasiparticles, exhibit a non-Fermi-liquid (NFL) phase associated with strange-metal behavior and high-temperature superconductivity, and display several additional remarkable properties that have also attracted considerable interest in gravitational physics. The primary objective of this part of the dissertation is to explain the self-tuning criticality of the NFL phase in the dissipative YSYK model. Although this phenomenon had previously been found by solving the exact Dyson–Schwinger equations (DSEs) in the infinite-particle limit, its origin has remained unexplained. To this end, we develop a functional renormalization group (FRG) approach for the dissipative YSYK model. Although the influence of lattice vibrations on electronic systems has been investigated for decades using well-established many-body and kinetic-theory methods, the behavior of strongly coupled electron–phonon systems remains incompletely understood. To address this problem, we study the microscopic Holstein model with dispersionless Einstein phonons at zero temperature. By combining the Dyson–Schwinger equations of the Holstein model with the exact FRG flow equations formulated within the chemical-potential cutoff scheme, we derive a Ward identity relating the electronic compressibility to the renormalized phonon frequency. This identity implies that the compressibility diverges when the renormalized phonon frequency vanishes, leading to a Pomeranchuk instability in the density channel with zero angular momentum. Using the nonperturbative FRG, we investigate the presence of this instability and propose a phase diagram of the Holstein model in arbitrary dimensions.