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.
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.
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.
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.
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.
Understanding the effects of disorder in quantum many-body systems is one of the central challenges of contemporary statistical physics. Its interplay with interactions and quantum fluctuations profoundly modifies the nature of quantum states and their dynamics, giving rise to phenomena such as localization, ergodicity breaking, and the emergence of complex collective behavior. This thesis presents new results on two classes of disordered quantum systems. The first part is devoted to the study of the many-body localization transition, a paradigmatic example of disorder-induced ergodicity breaking. The critical properties of the transition are investigated using a numerical renormalization-group approach, establishing a connection between its scaling behavior and that of the Anderson localization transition on tree-like graphs. The second part focuses on the zero-temperature quantum spin-glass phase of the two-dimensional bond-disordered Heisenberg model. Combining large-scale numerical simulations with a semiclassical expansion, evidence is provided for the existence of the spin-glass phase. The effective model governing the semiclassical fluctuations is further analyzed to characterize the low-energy excitation spectrum and its localization properties. Finally, the weak-disorder regime is investigated and its implications for the ferromagnetic phase are discussed. Overall, the results presented in this thesis contribute to the understanding of the effects of disorder in interacting quantum many-body systems, encompassing both localization phenomena and the collective behavior of disordered quantum magnets.
The main subjects of this dissertation are spin glass applications in other disciplines and spin glass algorithms. Spin glasses are magnetic systems with disorder and frustration, and the essential physics of spin glasses lies not in the details of their microscopic interactions but rather in the competition between quenched ferromagnetic and antiferromagnetic interactions. Concepts that arose in the study of spin glasses have led to applications in areas as diverse as computer science, biology, and finance, as well as a variety of others.\n\nIn the first part of this dissertation I study the equilibrium and non-equilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (a magnetic field). First, I perform finite-temperature Monte Carlo simulations in a field to test the robustness of the spin-glass phase and I show that the system has a spin-glass phase in a field, i.e., it exhibits a de Almeida–Thouless line. Then I study avalanche distributions when the system is driven by a field at zero temperature to test whether the system displays self-organized criticality. The numerical results suggest that avalanches (damage) can spread across the entire system with nonzero probability when the decay exponent of the interaction degree is less than or equal to 2, i.e., that Boolean decision problems on scale-free networks with competing interactions can be fragile when the system is not in thermal equilibrium.\n\nIn the second part of this dissertation I discuss the best-case performance of quantum annealers on native spin-glass benchmarks, i.e., how chaos can affect success probabilities. We perform classical parallel-tempering Monte Carlo simulations of the archetypal benchmark problem, an Ising spin glass, on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, I study the best-case resilience, or the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We compute the upper-bound success probabilities for different instance classes based on these simple error models, and I present strategies for developing robust and hard benchmark instances.\n\nIn the third part of this dissertation I present a cluster algorithm for Ising spin glasses that works in any space dimension and speeds up thermalization by several orders of magnitude at temperatures where thermalization is typically difficult. Our isoenergetic cluster moves are based on the Houdayer cluster algorithm for two-dimensional spin glasses and lead to a speedup over conventional state-of-the-art methods that increases with the system size. We illustrate the benefits (improved thermalization and achievement of more equiprobable sampling of ground states) of the isoenergetic cluster moves in two and three space dimensions, as well as in the nonplanar Chimera topology found in the D-Wave quantum annealing machine.\n\nFinally, I study the thermodynamic properties of the two-dimensional Edwards-Anderson Ising spin-glass model on a square lattice using the tensor renormalization group method based on a higher-order singular-value decomposition. Our estimates of the partition function without a high precision data type lead to negative values at very low temperatures, thus illustrating that the method can not be applied to frustrated magnetic systems.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.