Bosonization of Fermi liquids in a weak magnetic field

Abstract

Novel controlled non-perturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a {\em covariant Schwinger algebra}, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.

20 pages, 6 figures. Improved version. Two figures added. References updated. New section on forward scattering interactions added

References in corpus (11)

• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
• Quantum Oscillations in the Underdoped Cuprate YBa2Cu4O8
• A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor
• de Haas-van Alphen oscillations in the underdoped cuprate YBa${}_2$Cu${}_3$O${}_{6.5}$
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• Magnetotransport in a model of a disordered strange metal
• Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension
• Algebraic Approach to Fractional Quantum Hall Effect
• Pomeranchuk-Nematic instability in the presence of a weak magnetic field

Cited by in corpus (6)

• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Critical drag as a mechanism for resistivity
• Shear sound of two-dimensional Fermi liquids
• Cyclotron resonance and quantum oscillations of critical Fermi surfaces
• Two-dimensional Fermi liquid dynamics with density and quadrupolar interactions
• Probing Fermi liquid exceptional points through AC conductivity