Lectures on holographic non-Fermi liquids and quantum phase transitions (1110.3814v1)

Abstract: In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system arising from the duality, obtained by turning on a nonzero chemical potential for a U(1) global symmetry of a CFT, and described on the gravity side by a charged black hole. We address the following questions of such a finite density system: 1. Does the system have a Fermi surface? What are the properties of low energy excitations near the Fermi surface? 2. Does the system have an instability to condensation of scalar operators? What is the critical behavior near the corresponding quantum critical point? We find interesting parallels with those of high T_c cuprates and heavy electron systems. Playing a crucial role in our discussion is a universal intermediate-energy phase, called a "semi-local quantum liquid", which underlies the non-Fermi liquid and novel quantum critical behavior of a system. It also provides a novel mechanism for the emergence of lower energy states such as a Fermi liquid or a superconductor.

Analyzing Holographic Non-Fermi Liquids and Quantum Phase Transitions

The paper by Iqbal, Liu, and Mezei delves deeply into recent advancements in understanding non-Fermi liquids and novel quantum phase transitions using the framework of gauge/gravity duality. The authors explore finite density systems by examining the conventional charged black hole solution in Anti-de Sitter (AdS) space, which arises from introducing a nonzero chemical potential for a $U(1)$ global symmetry. This investigation is motivated by the intriguing parallels it can offer with condensed matter systems, specifically high-temperature superconductors such as high-$T_c$ cuprates and heavy electron systems.

Key Findings

The paper brings forth several insights about the nature of non-Fermi liquids and how quantum phase transitions can be comprehended through holography:

• Fermi Surface and Low-Energy Excitations: The research investigates whether the system possesses a Fermi surface and the nature of low-energy excitations in proximity to it. The holographic approach gives rise to a notion of a "semi-local quantum liquid" (SLQL). This phase does not conform to usual quasiparticle descriptions and presents a novel scenario for transition into conventional states such as Fermi liquids or superconductors.
• Instabilities and Quantum Critical Points: The paper identifies scalar operator condensation as a significant instability within the system, which leads to critical behaviors near associated quantum critical points. The authors suggest that the SLQL phase provides an innovative mechanism for the emergence of lower energy states such as Fermi liquids or superconductors.

Implications

The implications of these observations are both wide-ranging and crucial. Practically, this work might eventually aid in designing experiments or materials that harness the unique properties of these unconventional states, potentially leading to advances in superconductivity applications. Theoretically, the insights into quantum phase transitions could contribute to a better understanding of quantum entanglement and the holographic entropy as mechanisms for describing non-classical energy states.

The emergent picture highlights the intriguing role of geometry in understanding complex many-body dynamics. The holographic duality in these systems suggests that complex interactions at finite densities can be mapped to simplified gravitational problems, hinting at new paradigms in condensed matter physics. Furthermore, the evidence of potential non-Fermi liquid states might serve as a springboard for examining condensed matter systems with unconventional excitations and stability profiles.

Future Developments

For AI research and this holographic framework, the implications are multifold. Understanding these complex quantum states and transitions might influence algorithms for predictive modeling of physical systems. This could hold potential for developing AI applications in materials science and further exploring the crossover between classical physics insights and quantum computation challenges.

Moreover, the research accentuates the routes through which gravitational insights can inform practices in many-body quantum systems. As research progresses, one would expect that future theoretical and experimental findings might resolve questions about state transitions and stability, employing methods beyond the classical quasiparticle models, perhaps leveraging AI-driven analysis tools.

This paper is an essential contribution to the ongoing dialogue about holographic principles in quantum mechanics, expanding the conceptual framework of phase transitions and many-body system interactions. As our grasp of these intersections improves, we anticipate innovative developments that might bridge theoretical physics with practical applications comprehensively.