Indirect forces between impurities in one-dimensional quantum liquids

Abstract

We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction U the functional renormalization group method is used. For comparison we also study the U=0 case. We find that for a wide range of impurity parameters the impurity interaction V_{12} as a function of their separation r oscillates with decaying amplitude between being attractive and repulsive. For half-filling of the band and in a crossover regime between weak and strong impurities the interaction becomes purely attractive. For U=0 and independent of the impurity strength the amplitude of the interaction energy falls off as 1/r. For U>0 the decay for small separations and weak to intermediate impurities is governed by a U dependent exponent larger than -1, which crosses over to -1 for large r. The crossover scale depends on the impurity strength and U. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions U<0.

8 pages, 9 figures included

References in corpus (14)

• Confinement induced molecules in a 1D Fermi gas
• Friedel oscillations for interacting fermions in one dimension
• Resonant tunneling through a quantum dot weakly coupled to quantum wires or quantum Hall edge states
• The Fermi Edge Singularity and Boundary Condition Changing Operators
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Casimir forces between defects in one-dimensional quantum liquids
• Resonant tunneling of interacting electrons in a one-dimensional wire
• Transport of interacting electrons through a double barrier in quantum wires
• Functional renormalization group for Luttinger liquids with impurities
• Functional renormalization group approach to zero-dimensional interacting systems
• Oscillating Casimir force between impurities in one-dimensional Fermi liquids
• Correlation effects on resonant tunneling in one-dimensional quantum wires
• The two-boundary sine-Gordon model
• Interaction effects between impurities in low dimensional spin-1/2 antiferromagnets

Cited by in corpus (16)

• Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids
• Casimir effect in a one-dimensional gas of free fermions
• The Casimir-like effect in a one-dimensional Bose gas
• Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas
• Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas
• Casimir Effect for Massless Fermions in One Dimension: A Force Operator Approach
• Lattice-fermionic Casimir effect and topological insulators
• Phonon-mediated Casimir interaction between finite mass impurities
• Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas
• Casimir Interactions Between Scatterers in Metallic Carbon Nanotubes
• Classical Casimir force from a quasi-condensate of light
• T-matrix approach to the phonon-mediated Casimir interaction
• Dual chiral density wave induced oscillating Casimir effect
• Casimir effect in the nonequilibrium steady-state of a quantum spin chain
• Amplification phenomena of Casimir force fluctuations on close scatterers coupled via a coherent fermionic fluid
• Tuning long-range fermion-mediated interactions in cold-atom quantum simulators