Bosonization of Fermi liquids

Abstract

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.

42 pages, RevteX, preprint UIUC (1993)

References in corpus (4)

• Renormalization Group Approach to Interacting Fermions
• Bosonization and Fermion Liquids in Dimensions Greater Than One
• Bosonization of the Low Energy Excitations of Fermi Liquids
• Non-Analytic Contributions to the Self-Energy and the Thermodynamics of Two-Dimensional Fermi Liquids

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• Parquet solution for a flat Fermi surface
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• Quantum Quench and Prethermalization Dynamics in A Two-Dimensional Fermi Gas with Long-range Interactions
• Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
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• Geometrical Approach to Bosonization of D>1 Dimensional (Non) Fermi Liquids
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• Renormalization Group and Fermi Liquid Theory
• Heat Bath Approach to Landau Damping and Pomeranchuk Quantum Critical Points
• Competing Interactions, the Renormalization Group and the Isotropic-Nematic Phase Transition
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• Topological Multipartite Entanglement in a Fermi Liquid
• Correlation Energy of a Weakly Interacting Fermi Gas
• Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid
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• Lowest Landau level bosonization
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
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• The mobility and diffusion of a particle coupled to a Luttinger liquid
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• Interactions and Disorder in Multi-Channel Quantum Wires
• Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids
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• Universal Transverse Conductance between Quantum Hall Regions and (2+1)D Bosonization
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• Describing systems of interacting fermions by boson models: exact mapping in arbitrary dimension and applications
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• Functional Bosonization of Non-Relativistic Fermions in $(2+1)$ Dimensions
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• Why normal electrons with sufficiently singular interactions do not have a sharp Fermi surface
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• Theory of metal-insulator transitions in graphite under high magnetic field
• Phase space holography with no strings attached
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• Single-Particle Properties of a Two-Dimensional Fermi Liquid at finite Frequencies and Temperatures
• Calculation of the average Green's function of electrons in a stochastic medium via higher-dimensional bosonization
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• Competition between Pomeranchuk instabilities in the nematic and hexatic channels in a two-dimensional spinless Fermi fluid
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• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Disorder operators in two-dimensional Fermi and non-Fermi liquids through multidimensional bosonization
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