Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0002231 · Physical review. B, Condensed matter

Effect of Hund coupling on one-dimensional Luttinger liquids

H. C. Lee, Shuhui Yang

Published Jul 15, 2000• 1 citation
arXivHTMLPDF

Abstract

Two one-dimensional Luttinger liquid systems coupled by Hund coupling are studied by the renormalization-group and non-Abelian bosonization methods. It is found that the Hund coupling is always relevant irrespective of the repulsive interaction between electrons within each chain. The properties of the resulting strong coupling fixed point are discussed.

DOI
10.1103/physrevb.62.2372

Related papers

Renormalization-group study of Luttinger liquids with boundaries

S. Grap, V. Meden

We use Wilsons weak-coupling ``momentum'' shell renormalization-group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed irrelevant in the renormalization-group sense. Our study provides a more solid ground for many investigations of Luttinger liquids with open boundaries.

arXiv:0909.2095•Physical Review B•Nov 24, 2009•6 citations

Weak-coupling approach to hole-dopedS=1 Haldane systems

Satoshi Fujimoto, Norio Kawakami

As a weak-coupling analogue of hole-doped S=1 Haldane systems, we study two models for coupled chains via Hund coupling; coupled Hubbard chains, and a Hubbard chain coupled with an S=1/2 Heisenberg chain. The fixed point properties of these models are investigated by using bosonization and renormalization group methods. The effect of randomness on these fixed points is also studied. It is found that the presence of the disorder parameter inherent in the Haldane state in the former model suppresses the Anderson localization for weak randomness, and stabilizes the Tomonaga-Luttinger liquid state with the spin gap.

arXiv:cond-mat/9506118•Physical review. B, Condensed matter•Sep 1, 1995•26 citations

Phases of two coupled Luttinger liquids

Heinz J. Schulz

A model of two interacting one-dimensional fermion systems (``Luttinger liquids'') coupled by single-particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising-type critical sector. For general repulsive interactions, there is a spin excitation gap and either d-type pairing or orbital antiferromagnetic fluctuations dominate. It is argued that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many-chain system is discussed. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9412098•Physical review. B, Condensed matter•Feb 1, 1996•193 citations

Renormalization of the Coulomb interaction in one-dimensional electron systems

Stefano Bellucci A, J. González

Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model, as well as renormalization of the Fermi velocity. This may have significant effects depending on the filling level of the system. The effective couplings remain bounded at arbitrarily low energies so that, in spite of the long-range character of the interaction, the system still falls into the Luttinger liquid universality class.

arXiv:cond-mat/9802011•Feb 2, 1998•0 citations

Kondo effect in a Tomonaga-Luttinger liquid

Akira Furusaki, Naoto Nagaosa

The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.

Physical Review Letters•Feb 7, 1994•204 citations

Ferromagnetic fixed point of the Kondo model in a Luttinger liquid

Mun Dae Kim, Chul Koo Kim, Kyun Nahm +1 more

The Kondo effect in a Luttinger liquid is studied using the renormalization group method. By renormalizing the boson fields, scaling equations to the second order for an arbitrary Luttinger interaction are obtained. For the ferromagnetic Kondo coupling, a spin bound state (triplet) can be realized without invoking a nearest neighbour spin interaction in agreement with the recent Bethe ansatz calculation. The scaling theory in the presence of the scalar potential shows that there is no interplay between the magnetic and non-magnetic interaction. Also a study on the crossover behaviour of the Kondo temperature between the exponential and the power-law type is presented.

arXiv:cond-mat/0103153•Journal of Physics Condensed Matter•Mar 22, 2001•3 citations
Two one-dimensional Luttinger liquid systems coupled by Hund coupling are studied by the renormalization-group and non-Abelian bosonization methods. It is found that the Hund coupling is always relevant irrespective of the repulsive interaction between electrons within each chain. The properties of the resulting strong coupling fixed point are discussed.
As a weak-coupling analogue of hole-doped S=1 Haldane systems, we study two models for coupled chains via Hund coupling; coupled Hubbard chains, and a Hubbard chain coupled with an S=1/2 Heisenberg chain. The fixed point properties of these models are investigated by using bosonization and renormalization group methods. The effect of randomness on these fixed points is also studied. It is found that the presence of the disorder parameter inherent in the Haldane state in the former model suppresses the Anderson localization for weak randomness, and stabilizes the Tomonaga-Luttinger liquid state with the spin gap.
A model of two interacting one-dimensional fermion systems (``Luttinger liquids'') coupled by single-particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising-type critical sector. For general repulsive interactions, there is a spin excitation gap and either d-type pairing or orbital antiferromagnetic fluctuations dominate. It is argued that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many-chain system is discussed. \textcopyright{} 1996 The American Physical Society.
Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model, as well as renormalization of the Fermi velocity. This may have significant effects depending on the filling level of the system. The effective couplings remain bounded at arbitrarily low energies so that, in spite of the long-range character of the interaction, the system still falls into the Luttinger liquid universality class.
The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.
The Kondo effect in a Luttinger liquid is studied using the renormalization group method. By renormalizing the boson fields, scaling equations to the second order for an arbitrary Luttinger interaction are obtained. For the ferromagnetic Kondo coupling, a spin bound state (triplet) can be realized without invoking a nearest neighbour spin interaction in agreement with the recent Bethe ansatz calculation. The scaling theory in the presence of the scalar potential shows that there is no interplay between the magnetic and non-magnetic interaction. Also a study on the crossover behaviour of the Kondo temperature between the exponential and the power-law type is presented.