Unveiling Dirty Quantum Criticality with Hart Goldman from MIT

Table of Contents

1. Introduction
2. The Conventional Wisdom
3. Anomalous Metals
4. Quantum Critical Points
5. Evidence for Anomalous Metallic Phases
6. The Role of Disorder, Interactions, and Quantum Criticality
7. The Two Paths Forward
8. Targeting the Anomalous Metallic Regime
9. Targeting the Quantum Critical Regime
10. Dirty Bosonic Quantum Criticality
11. Screening of Disorder by Interactions
12. Quantum Corrections and the Running of Disorder
13. The New Dirty Quantum Critical Point
14. Properties of the Dirty Quantum Critical Point
15. Future Directions
16. Conclusion

Dirty Quantum Critical Points: Exploring the Interplay of Disorder and Interactions

In the field of condensed matter physics, there has been a long-standing debate regarding the existence of metallic ground states in two-dimensional (2D) systems at zero temperature. According to the conventional wisdom, the absence of spin-orbit coupling implies the absence of metallic ground states in 2D. However, experimental observations of anomalous metals in various material contexts have challenged this conclusion. These anomalous metallic phases are often observed near quantum critical points, which themselves have mysterious behavior.

In this article, we will Delve into the interplay of disorder, interactions, and quantum criticality in 2D systems. We will explore the possibility of a dirty quantum critical point, where disorder and interactions balance each other, leading to an intriguing phase that defies the conventional understanding of localization and metallicity. Through a careful examination of the screening effects of interactions and the quantum corrections induced by disorder, we will uncover the emergence of a new dirty quantum critical point.

Introduction

The absence of metallic ground states in 2D systems at zero temperature has long been considered the prevailing understanding in the field of condensed matter physics. This conclusion stems from the scaling theory of localization, which suggests that non-interacting electrons with weak disorder do not exhibit metallic behavior in 2D. However, recent experimental observations of anomalous metals challenge this conventional wisdom.

Anomalous metallic phases have been observed in various material contexts, such as quantum hall systems, superconducting thin films near the superconductor-insulator transition, and quantum spin Hall to superconductor transitions. These anomalous metallic phases often occur near quantum critical points, which exhibit mysterious behavior.

In this article, we aim to explore the interplay of disorder, interactions, and quantum criticality in 2D systems. By considering the anomalous metallic regime and the quantum critical regime, we will investigate the possibility of a dirty quantum critical point. This dirty quantum critical point represents a balance between disorder and interactions in a way that defies the conventional understanding of localization and metallicity.

The Conventional Wisdom

The conventional wisdom in the field states that metallic ground states are absent in 2D systems at zero temperature, at least in the absence of spin-orbit coupling. This conclusion is derived from the scaling theory of localization, which predicts that non-interacting electrons with weak disorder do not exhibit metallic behavior in 2D.

However, experimental observations have consistently defied this conclusion. Anomalous metallic phases have been observed in various contexts, including quantum hall systems, superconducting thin films near the superconductor-insulator transition, and quantum spin Hall to superconductor transitions. These anomalous metallic phases occur near quantum critical points and challenge the conventional understanding of metallicity in 2D systems.

Anomalous Metals

Anomalous metals are a specific class of materials that display metallic behavior in spite of the absence of spin-orbit coupling. These materials have been observed in a variety of contexts, including quantum hall systems near the fractional quantum Hall effect, superconducting thin films near the superconductor-insulator transition, and quantum spin Hall to superconductor transitions in transition metal dichalcogenides.

One unifying feature of these anomalous metallic phases is their proximity to quantum critical points, which themselves exhibit peculiar behavior. The behavior near these quantum critical points is characterized by critical exponents and emergent symmetries that are not typically found together in theoretical constructions.

Quantum Critical Points

Quantum critical points are the phase transitions that occur at absolute zero temperature when a system undergoes a change in its ground state. These critical points exhibit a range of unusual phenomena and are of great interest in the field of condensed matter physics. Near these quantum critical points, exotic behavior can manifest, including a breakdown of conventional metallic behavior and the emergence of anomalous metallic phases.

One key characteristic of quantum critical points is their mysterious behavior. Critical exponents, which describe the scaling properties of various physical quantities near the critical point, often exhibit peculiar values that are not easily explained by existing theoretical frameworks.

Evidence for Anomalous Metallic Phases

Experimental observations of anomalous metallic phases have been instrumental in challenging the conventional wisdom regarding metallic ground states in 2D systems. These observations provide empirical evidence for the existence of metallic behavior even in the absence of spin-orbit coupling.

Some notable examples of anomalous metallic behavior include the fractional quantum Hall effect near a filling factor of one-half, the superconductor-insulator transition in disordered superconducting thin films, and the quantum spin Hall to superconductor transitions in transition metal dichalcogenides. These experimental findings defy the predictions of the scaling theory of localization and call for a deeper understanding of the interplay between disorder, interactions, and quantum criticality.

The Role of Disorder, Interactions, and Quantum Criticality

The existence of anomalous metallic phases near quantum critical points raises important questions about the interplay between disorder, interactions, and quantum criticality. The conventional understanding suggests that disorder and interactions alone cannot account for the observed phenomena, prompting researchers to consider more complex theoretical frameworks.

Two possible paths forward have been identified to tackle this problem. The first path involves directly targeting the anomalous metallic regime by studying systems with disorder and interactions at the Fermi surface. However, this approach is challenging due to the inherent difficulty of dealing with disorder, which tends to introduce a finite diffusive scattering rate and destabilize the metallic behavior.

The Second path focuses on studying the quantum critical regime, where Scale invariance allows for the subversion of the physics of localization. This approach is more tractable as the diverging localization length counteracts the effects of disorder, leading to a new fixed point at the quantum critical point.

The Two Paths Forward

To unravel the mystery of anomalous metallic phases and their connection to quantum critical points, researchers have pursued two distinct paths. The first path involves directly studying the anomalous metallic regime, where disorder and interactions are inextricably intertwined. However, this path presents significant challenges due to the intrinsic difficulties associated with disorder and the tendency for metallic behavior to flow to strong disorder and interact with disorder in general.

The second path focuses on the quantum critical regime, where the scale invariance of the system allows for a better understanding of disorder, interactions, and quantum criticality. By targeting the quantum critical point, researchers can study the emergent properties of the system and gain insights into the complex interplay between disorder and interactions.

Targeting the Anomalous Metallic Regime

Research efforts have been devoted to directly targeting the anomalous metallic regime in order to gain insights into the interplay of disorder and interactions. This approach involves studying systems with disorder and interactions at the Fermi surface, where the effects of disorder are prominent and can potentially stabilize metallic behavior.

However, achieving a comprehensive understanding of the anomalous metallic regime remains a significant challenge. Disorder tends to introduce a finite diffusive scattering rate, making the study of metallic behavior in 2D systems difficult. Despite recent progress in this area, further research is needed to fully uncover the underlying mechanisms driving anomalous metallic phases.

Targeting the Quantum Critical Regime

An alternative approach to understanding the interplay between disorder and interactions is to target the quantum critical regime. At the quantum critical point, the system exhibits scale invariance, which results in a diverging localization length and allows for the study of disorder and interactions at a new fixed point.

By focusing on the quantum critical regime, researchers can bypass the challenges posed by disorder and gain valuable insights into the emergent properties of the system. The study of quantum critical points offers the potential to uncover new organizing principles for the interplay of disorder and interactions, shedding light on the mysterious behavior observed near these points.

Dirty Bosonic Quantum Criticality

One particularly intriguing aspect of the interplay between disorder and interactions is the phenomenon of dirty bosonic quantum criticality. In this Scenario, a system of bosons undergoes a superfluid-insulator transition at zero temperature, and disorder is introduced in the form of a random mass that couples to the square of the order parameter.

Traditionally, disorder is considered Relevant in systems with three or more bosonic species, while interactions between the bosons tend to drive the system to strong disorder. However, by studying the large-end limit of this model, a new phenomenon emerges. The disorder is screened by interactions, resulting in a fixed point where disorder is exactly marginal.

Screening of Disorder by Interactions

One of the key phenomena observed in the study of dirty bosonic quantum criticality is the screening of disorder by interactions. As the system flows to the Wilson-Fisher fixed point, the disorder becomes increasingly short-ranged compared to its original form. This screening effect is a consequence of the balancing act between disorder and interactions and leads to the emergence of a new fixed point with marginal disorder.

The screening of disorder by interactions has significant implications for the behavior of the system near the quantum critical point. It allows for the stabilization of metallic behavior and the exploration of Novel phenomena that defy the conventional understanding of localization and metallicity.

Quantum Corrections and the Running of Disorder

In addition to the screening of disorder by interactions, quantum corrections also play a crucial role in the study of dirty bosonic quantum criticality. These corrections arise from the interplay between interactions and disorder and result in the running of the disorder coupling.

Quantum corrections destabilize the fixed point and give rise to a new dirty quantum critical point. The beta function governing the running of the disorder coupling has a negative value, indicating a shift away from the stability of the fixed point. This negative beta function leads to intriguing renormalization group flows and the emergence of a new fixed point with novel properties.

The New Dirty Quantum Critical Point

The study of dirty bosonic quantum criticality has revealed the existence of a new dirty quantum critical point. At this point, the system exhibits a delicate balance between disorder and interactions, resulting in a unique phase of matter with properties that challenge the conventional understanding of localization and metallicity.

The dirty quantum critical point is characterized by specific values of critical exponents, emergent symmetries, and transport behavior. These properties offer valuable insights into the interplay between disorder, interactions, and quantum criticality and pave the way for further exploration of the physics of dirty quantum criticality.

Properties of the Dirty Quantum Critical Point

The dirty quantum critical point possesses several intriguing properties that distinguish it from conventional quantum critical points and metallic phases. The correlation length exponent, which describes the scaling behavior of correlations near the critical point, exhibits a delicate balancing act between disorder and interactions. This balance is reflected in critical exponents and emergent symmetries that deviate from those of traditional quantum critical points.

The relationship between disorder, interactions, and quantum criticality at the dirty quantum critical point is still not fully understood. However, ongoing research aims to unravel the complex interplay between these factors and shed light on the emergent properties of the system.

Future Directions

The study of dirty quantum critical points has opened up exciting avenues for future research. There are numerous unanswered questions and unexplored phenomena that warrant further investigation.

Some potential future directions include the investigation of universal transport properties at the dirty quantum critical point. Understanding the behavior of conductivity, resistivity, and emergent symmetries in this regime can provide valuable insights into the nature of dirty quantum criticality.

Additionally, the study of dirty quantum criticality in other material contexts and the exploration of disorders beyond the ones considered here will provide further insights into the interplay of disorder, interactions, and quantum criticality.

Conclusion

In this article, we have explored the interplay between disorder, interactions, and quantum criticality in 2D systems. By studying the phenomenon of dirty bosonic quantum criticality, we have gained valuable insights into the emergence of new phases of matter and their connection to quantum critical points.

The discovery of the dirty quantum critical point challenges the prevailing understanding of metallic behavior in 2D systems and provides a new framework for exploring the physics of disorder, interactions, and quantum criticality.

While much progress has been made, there are still many open questions and avenues for further research. By continuing to investigate the properties and phenomena associated with dirty quantum criticality, we can Deepen our understanding of complex quantum systems and uncover new organizing principles for the interplay of disorder and interactions.