Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals (1503.00732v2)

Abstract: A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density...

• The paper presents magnetic catalysis as a key mechanism where external fields induce dimensional reduction and spontaneous symmetry breaking.
• Analytical methods and lattice simulations rigorously validate the theoretical framework in QCD and high-energy physics contexts.
• Insights extend to graphene and Dirac semimetals, offering a unified approach to understanding magnetic field effects on electronic properties.

Overview of Quantum Field Theory in a Magnetic Field with Applications in QCD and Condensed Matter Systems

This paper extensively reviews quantum field theoretical phenomena influenced by external magnetic fields, focusing on their applications both in relativistic systems, such as quantum chromodynamics (QCD), and in quasirelativistic condensed matter systems, including graphene and Dirac/Weyl semimetals. The central theme revolves around theoretical constructs like magnetic catalysis—an effect where external magnetic fields can enhance or induce spontaneous symmetry breaking by affecting low-energy relativistic fermions. The review elaborates on theoretical frameworks and subsequently correlates these with phenomenological implications in several domains ranging from heavy-ion collisions to technological applications in materials like graphene and Dirac metals.

Magnetic Catalysis and Dimensional Reduction

A detailed discussion is provided about the concept of magnetic catalysis, where external magnetic fields facilitate the generation of fermion masses. A key mechanism underlying this phenomenon is the magnetic-field-induced dimensional reduction, where the dynamics of charged relativistic fermions become effectively lower-dimensional because of the magnetic field. This reduction is critical in understanding the enhanced fermion-antifermion pairing dynamics, leading to spontaneous symmetry breaking.

Applications to QCD and Beyond

The review intricately examines the phenomenon within the realms of quantum electrodynamics (QED) and QCD, making bold claims about the influence of magnetic catalysis on high-energy physics, for instance, in altering phase transitions in QCD under extreme conditions. Additionally, it evaluates the predictive power of these theoretical frameworks, using rigorous lattice simulations that probe the implications of magnetic catalysis in QCD-like settings.

Implications for Condensed Matter Physics

The insights from magnetic catalysis are extended to condensed matter physics by examining its role in understanding the electronic properties of materials like graphene and Dirac/Weyl semimetals. In these systems, the paper illustrates how external magnetic fields can modify electronic states, leading to phenomena such as the quantum Hall effect. The discussion in this context is enriched by incorporating the concept of generalized magnetic catalysis, which unifies various symmetry-breaking order parameters, previously thought to be independent.

Analytical and Numerical Approaches

The research also applies analytical quantum field theory methodologies and highlights results obtained from lattice simulations to verify the theoretical claims made, especially in the non-ablation phases of QCD and reduced dimensions models analogous to condensed matter systems. Such crossover studies present promising directions for future computational endeavors and experimental verifications.

Conclusion and Future Directions

The conclusions drawn emphasize that magnetic fields are potent drivers of symmetry-breaking transitions across various physical domains. The universality of the magnetic catalysis effect suggests potentially groundbreaking applications in material science and high-energy physics. Future research could focus on experimental validations of these theoretical predictions and further exploration of noncommutative field theories, as suggested by the implications of external magnetic fields on quantum theories.

In summary, the paper acts as a bridge connecting quantum field theoretical predictions with practical phenomena observed in both fundamental and applied physics, contributing a substantial analytical foundation for ongoing and future explorations in magnetically influenced systems.