Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity

Abstract

Using bosonization-fermionization transformation we map the Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the model of fermionic quasiparticles whose interaction is irrelevant in the renormalization group sense. Such mapping allows us to set up an expansion for the density-density propagator of the original Tomonaga-Luttinger Hamiltonian in orders of the (irrelevant) quasiparticle interaction. The lowest order term in such an expansion is proportional to the propagator for free fermions. The next term is also evaluated. The propagator found is used for calculation of the Coulomb drug resistivity $r$ in a system of two capacitively coupled one-dimensional conductors. It is shown that $r$ is proportional to $T^2$ for both free and interacting fermions. The marginal repulsive in-chain interaction acts to reduce $r$ as compared to the non-interacting result. The correction to $r$ due to the quasiparticle interaction is found as well. It scales as $T^4$ at low temperature.

5 pages, 1 eps figure; the new version of the e-print corrects an error, which exists in the original submission; fortunately, all important conclusions of the study remain valid

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Cited by in corpus (21)

• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Universal theory of nonlinear Luttinger liquids
• Coulomb drag
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Universal broadening of the light cone in low-temperature transport
• Separation of Timescales in a Quantum Newton's Cradle
• Coulomb drag between ballistic quantum wires
• Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature
• Relaxation in Luttinger liquids: Bose-Fermi duality
• Dissipationless kinetics of one dimensional interacting fermions
• Equilibration in one-dimensional quantum hydrodynamic systems
• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• Thermal Transport in One Dimensional Electronic Fluid
• Coulomb drag between helical Luttinger liquids
• Equilibration in a chiral Luttinger liquid
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• Ultranarrow resonance in Coulomb drag between quantum wires at coinciding densities
• Different types of the dimensional crossover in the quasi-one-dimensional spinless fermion systems
• One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Nonlinear edge transport in a quantum Hall system