Strong Magnetic Fields Restore Broken Symmetries in Relativistic Dirac Fermion Systems

The behaviour of fundamental particles in strong magnetic fields presents a long-standing challenge in theoretical physics, and new research sheds light on this complex interaction. Thomas Dumitrescu from the Mani L. Bhaumik Institute for Theoretical Physics at UCLA, along with Juan Maldacena from the Institute for Advanced Study, Princeton, investigate the dynamics of massless particles responding to both a magnetic field and light. Their work reveals that under these conditions, the fundamental vacuum state spontaneously loses symmetry, a phenomenon with implications for understanding the behaviour of matter in extreme astrophysical environments. By adapting techniques originally developed for studying materials exhibiting Hall magnetism, the researchers determine the spectrum of resulting excitations and construct a comprehensive description of the low-energy behaviour of these particles.

Dirac Fermions and Photons in Magnetic Fields

Researchers explore the behaviour of massless Dirac fermions interacting with a propagating photon in two dimensions when a uniform magnetic field is present. This system allows for an exact solution, providing insights into non-perturbative phenomena within quantum electrodynamics. The investigation focuses on understanding how the magnetic field alters the interactions between the fermions and the photon, modifying the system’s overall behaviour. Studying the system in two dimensions simplifies calculations while retaining the essential physics of the interaction. The presence of a magnetic field introduces a characteristic length scale, enabling the investigation of phenomena such as magnetic screening and the formation of bound states.

When the magnetic field is sufficiently strong, researchers find that the vacuum spontaneously breaks certain global symmetries. They also determine the spectrum of excitations around this vacuum and calculate the resulting low-energy effective action. The techniques employed build upon those previously developed for quantum Hall ferromagnets in condensed matter physics.

Anomalies Drive Topological Matter Phases

This extensive research paper presents a comprehensive overview of ideas and connections within condensed matter physics and quantum field theory. It explores the role of anomalies, violations of classical symmetries at the quantum level, in driving and characterizing topological phases of matter. The paper delves into the connection between the Quantum Hall Effect (QHE), topological order, and the emergence of anyons, particles with exotic exchange statistics, and discusses Skyrmions and their role in understanding the QHE.

The use of effective field theories (EFTs) to describe low-energy physics is emphasized, with the derivative expansion used to analyze quantum field theories in various dimensions. The paper stresses the importance of global symmetries and how their anomalies can lead to interesting physical phenomena, including discussions of time-reversal symmetry and chiral symmetry. A major thread is the interplay between condensed matter physics and quantum field theory, highlighting how concepts from QFT, like anomalies, duality, and effective field theories, can be applied to understand phenomena in condensed matter systems, and vice versa.

The paper repeatedly emphasizes how anomalies can drive the emergence of topological phases, linking the axial anomaly to the emergence of chiral edge states in topological insulators. Duality is presented as a powerful tool for revealing hidden symmetries and simplifying complex problems, highlighting the deep connection between symmetry and topology.

Magnetic Fields Induce Symmetry Breaking and Excitations

This research investigates the behaviour of massless Dirac fermions interacting with a magnetic field in two dimensions, revealing how strong magnetic fields induce spontaneous breaking of symmetries within the system. The study demonstrates that at high magnetic fields, the theory simplifies, allowing for the identification of light particle excitations, including Nambu-Goldstone bosons, which emerge due to the broken symmetries. Importantly, the parameters governing the behaviour of these excitations can be calculated directly from the underlying theory, and the low-energy behaviour aligns with expected anomalies.

The findings extend to scenarios with multiple fermion flavours, showing that increasing the number of flavours influences the system’s response to the magnetic field. With a large number of flavours, the theory transitions towards a weakly-coupled conformal field theory, and even a small magnetic field can induce symmetry breaking.