Disorder in quantum many-body physics: from strange metal to spin glass systems

Abstract

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.