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Transport, criticality, and chaos in fermionic quantum matter at nonzero density

Aavishkar A. Patel

Published Apr 23, 2019• 1 citation
OpenAlex

Abstract

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.

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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.
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 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 NNN 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.
Significance All high-temperature superconductors exhibit a remarkable “strange metal” state above their critical temperatures. A theory of the strange metal is a prerequisite for a deeper understanding of high-temperature superconductivity, but the ubiquitous quasiparticle theory of normal metals cannot be extended to the strange metal. Instead, strange metals exhibit many-body chaos over the shortest possible time allowed by quantum theory. We characterize the quantum chaos in a model of fermions at nonzero density coupled to an emergent gauge field. We find a universal relationship between the chaos parameters and the experimentally measurable thermal diffusivity. Our results establish a connection between quantum dephasing and energy transport in states of quantum matter without quasiparticles.
We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the ttt-JJJ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large NNN theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions.
Modern quantum materials host a wide range of electronic phases in which transport properties are governed by strong interactions and collective effects. This thesis investigates charge, heat, and momentum transport in interacting electronic systems across different theoretical frameworks, ranging from Fermi liquid theory to strongly coupled strange metals.The first part of the thesis focuses on two-dimensional Fermi liquids at finite temperature, where rapid electron-electron scattering can give rise to hydrodynamic behavior. A kinetic-theory framework allowing an exact treatment of quasiparticle distribution functions beyond the asymptotic low-temperature regime is used to compute the full spectrum of collective modes, providing a detailed characterization of long-lived odd-parity excitations and the intermediate transport regime between ballistic and hydrodynamic flow. The same framework is employed to determine the shear viscosity of interacting electron liquids beyond conventional perturbative limits.The second part of the thesis concerns strongly interacting quantum systems where the quasiparticle picture breaks down.Holographic duality is used to study transport and thermoelectric response in quantum critical systems subject to periodic potentials, providing a controlled framework for momentum relaxation and magnetotransport in non-Fermi liquids. The thesis further develops holographic models of collective charge dynamics in systems with dynamical electromagnetism, including bulk plasmons and surface plasmon polaritons, and explores connections between Fermi surface physics and holographic gauge-field dynamics.
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.