Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Abstract

a b s t r a c tA 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. Finally, we discuss the interplay between relativistic quantum field theories (including quantum electrodynamics and quantum chromodynamics) in a magnetic field and noncommutative field theories, which leads to a new type of the latter, nonlocal noncommutative field theories.

Strong magnetic fields in a nonlocal Polyakov chiral quark model

“…Indeed, contrary to what happens e.g. in the standard local NJL model [4][5][6], in our models the chiral restoration critical temperature becomes lower as the external magnetic field is increased. This is related with the fact that the condensates do not show in general a monotonic 7 EPJ Web of Conferences 172, 02007 (2018) https://doi.org/10.1051/epjconf/201817202007 ISMD 2017 increase with B for a fixed value of the temperature.…”

The evolution of meson masses in a strong magnetic field

“…However, as shown in [82], the colormagnetic fields cannot violate the positivity of the qq spectra, implying that some sort of the cut-off parameter must occur in the whole perturbative series with nonperturbative background. Moreover, PIH method has a natural dimensional cutoff parameter for color field λ 1 GeV −1 -correlation length of the vacuum gluonic background, which should be used to smear δ-function in (5.1) [83] 2) and after the averaging with the CS meson wave function (2.17) one obtains the spin-spin matrix element…”

“…a recent review [1,2]. When MF is not ultra-intense (eB σ, where σ = 0.18 GeV 2 is a confinement string tension), 1 the main characteristics related to the behavior of hadrons in MF are magnetic moments and magnetic susceptibilities, while for the strong MF limit (eB ≥ σ) the hadron energy and width depend on MF directly.…”

“…On the theoretical side the main directions of research in this area are the lattice studies [20,21]- [31], [32]- [43], the chiral Lagrangians with MF [44]- [50,51], effective hadron Lagrangians [1,2,[52][53][54][55][56], [57]- [60], and recently developed path integral Hamiltonians (PIH) [62]- [68], and the chiral Lagrangian with quark degrees of freedom [69].…”

Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene

“…native scenarios utilizes the idea of magnetic catalysis (MC) [33][34][35] . The corresponding order parameters are excitonic (particle-hole) condensates responsible for the generation of the Dirac and/or Haldane masses of quasiparticles 6,[36][37][38][39][40][41][42][43] .…”