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

Journal of Physics A Mathematical and General

Exact solution for a one-dimensional multichannel model of correlated electrons with an Anderson-like impurity

Andrei A. Zvyagin, P. Schlottmann

Published Feb 27, 1998• 6 citations
Publisher

Abstract

We study a one-dimensional n -channel highly correlated electron model (based on the supersymmetric t-J model) with a magnetic impurity of arbitrary spin S that can hybridize with up to one itinerant electron per channel. The model extends the multichannel Kondo problem to correlations in the host and to the mixed valence regime. The Bethe ansatz equations are derived and solved for the ground state and for low temperatures. We conclude that the critical non-Fermi-liquid (overscreened) behaviour cannot be reached for this interacting electron system. Possible applications of the model are discussed.

DOI
10.1088/0305-4470/31/8/010

Related papers

Exact solution for an exchange impurity in a one-dimensional correlated host

Andrei A. Zvyagin, P. Schlottmann

The one-dimensional t - J model at the supersymmetric point, J = 2t, with a magnetic impurity of arbitrary spin S is studied exactly using the Bethe ansatz technique. The impurity interacts by spin exchange with the electrons on neighbouring sites of a lattice without destroying the integrability. The discrete Bethe ansatz equations diagonalizing the model, and the thermodynamic equations are derived. The impurity free energy is obtained for arbitrary band filling as a function of temperature and external magnetic field. The impurity can localize up to one itinerant hole, and has in general mixed-valent properties.

Journal of Physics Condensed Matter•Apr 28, 1997•31 citations

Integrable supersymmetric t-J model with magnetic impurity

P. Schlottmann, Andrei A. Zvyagin

We consider the one-dimensional t-J model, which consists of spin-1/2 electrons on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J=2t. We extend the model by introducing an impurity of arbitrary spin S that interacts with the electrons on the neighboring sites without destroying the integrability. The lattice model is defined by the scattering matrices via the quantum inverse scattering method. The interaction Hamiltonian between the impurity and the itinerant electrons is only explicitly constructed in the continuum limit. The discrete Bethe ansatz equations diagonalizing the model are derived and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived and the impurity free energy is obtained for arbitrary bandfilling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter. The impurity can localize up to one itinerant electron and has in general mixed valent properties. The integer valent low T small H fixed point of the impurity corresponds to an asymptotically free spin S, while if either T or H (or both) become large the impurity behaves like an asymptotically free spin (S+).

Physical review. B, Condensed matter•Feb 15, 1997•56 citations

Multichannel Anderson impurity behavior in a pure hybridization impurity model

Jianhui Dai

A single multichannel quantum impurity model with pure hybridizations between the localized and orbital degenerate conducting electrons is shown to exhibit several interesting impurity properties resembling that of the multichannel Anderson model. Particularly for two special kinds of hybridization parameters the model can be solved exactly by the Bethe ansatz method. In these integrable cases, the competition between the direct and exchange correlated hybridizations can produces either a Fermi-liquid or non-Fermi-liquid behavior at low temperatures.

Physical Review B•Dec 1, 2004•1 citation

Magnetic impurity in the one-dimensional Hubbard model

Andrei A. Zvyagin, P. Schlottmann

The Hubbard chain with a magnetic impurity of arbitrary spin $S$ is studied using the Bethe ansatz technique. We consider two kinds of impurities which interact with itinerant electrons on the neighboring lattice sites without destroying the integrability. The correlations in the host always induce valence fluctuations at the impurity site. For a repulsive Hubbard $U$, an impurity coupled via antiferromagnetic exchange to the host reveals magnetic properties similar to those of the ordinary Kondo effect. In contrast, a hybridization impurity (Anderson-like) embedded into the attractive Hubbard model gives rise to essentially different magnetic behavior. This difference is a consequence of the spin gap in the host.

Physical review. B, Condensed matter•Jul 1, 1997•38 citations

One-dimensional heavy fermion lattice model

Andrei A. Zvyagin, P. Schlottmann

We consider a one-dimensional supersymmetric t−J model and introduce a finite concentration of impurities of arbitrary spin S without destroying the integrability. Using the Bethe ansatz equations diagonalizing the correlated host with impurities, we discuss the ground state properties as a function of magnetic field H and the Kondo exchange coupling. While an isolated impurity of spin S>1/2 has a magnetic ground state of effective spin (S−12), a finite concentration introduces a heavy impurity band and yields a singlet ground state with antiferromagnetically correlated impurities. A field H first polarizes the narrow impurity band. The impurities have mixed valent properties induced in part by correlations in the host. Some aspects of the model are related to heavy fermion alloys.

Journal of Applied Physics•Apr 15, 1999•0 citations

Multichannel Kondo problem and some applications

P. Schlottmann, Pedro D Sacramento

We review analytical and numerical results derived from the Bethe ansatz solution of the n-channel Kondo model of arbitrary spin S as a function of temperature, external field, impurity spin S and the number of channels n. Three situations have to be distinguished: (i) If n = 2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n < 2S the impurity spin is only partially compensated (undercompensated), and (iii) if n > 2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are discussed in the context of magnetic impurities, e.g. Fe, Cr and Tm in simple metals, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian Heisenberg model and electron assisted-tunnelling of an atom in a double-well potential.

Advances In Physics•Dec 1, 1993•167 citations
We study a one-dimensional n -channel highly correlated electron model (based on the supersymmetric t-J model) with a magnetic impurity of arbitrary spin S that can hybridize with up to one itinerant electron per channel. The model extends the multichannel Kondo problem to correlations in the host and to the mixed valence regime. The Bethe ansatz equations are derived and solved for the ground state and for low temperatures. We conclude that the critical non-Fermi-liquid (overscreened) behaviour cannot be reached for this interacting electron system. Possible applications of the model are discussed.
The one-dimensional t - J model at the supersymmetric point, J = 2t, with a magnetic impurity of arbitrary spin S is studied exactly using the Bethe ansatz technique. The impurity interacts by spin exchange with the electrons on neighbouring sites of a lattice without destroying the integrability. The discrete Bethe ansatz equations diagonalizing the model, and the thermodynamic equations are derived. The impurity free energy is obtained for arbitrary band filling as a function of temperature and external magnetic field. The impurity can localize up to one itinerant hole, and has in general mixed-valent properties.
We consider the one-dimensional t-J model, which consists of spin-1/2 electrons on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J=2t. We extend the model by introducing an impurity of arbitrary spin S that interacts with the electrons on the neighboring sites without destroying the integrability. The lattice model is defined by the scattering matrices via the quantum inverse scattering method. The interaction Hamiltonian between the impurity and the itinerant electrons is only explicitly constructed in the continuum limit. The discrete Bethe ansatz equations diagonalizing the model are derived and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived and the impurity free energy is obtained for arbitrary bandfilling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter. The impurity can localize up to one itinerant electron and has in general mixed valent properties. The integer valent low T small H fixed point of the impurity corresponds to an asymptotically free spin S, while if either T or H (or both) become large the impurity behaves like an asymptotically free spin (S+).
A single multichannel quantum impurity model with pure hybridizations between the localized and orbital degenerate conducting electrons is shown to exhibit several interesting impurity properties resembling that of the multichannel Anderson model. Particularly for two special kinds of hybridization parameters the model can be solved exactly by the Bethe ansatz method. In these integrable cases, the competition between the direct and exchange correlated hybridizations can produces either a Fermi-liquid or non-Fermi-liquid behavior at low temperatures.
The Hubbard chain with a magnetic impurity of arbitrary spin SSS is studied using the Bethe ansatz technique. We consider two kinds of impurities which interact with itinerant electrons on the neighboring lattice sites without destroying the integrability. The correlations in the host always induce valence fluctuations at the impurity site. For a repulsive Hubbard UUU, an impurity coupled via antiferromagnetic exchange to the host reveals magnetic properties similar to those of the ordinary Kondo effect. In contrast, a hybridization impurity (Anderson-like) embedded into the attractive Hubbard model gives rise to essentially different magnetic behavior. This difference is a consequence of the spin gap in the host.
We consider a one-dimensional supersymmetric t−J model and introduce a finite concentration of impurities of arbitrary spin S without destroying the integrability. Using the Bethe ansatz equations diagonalizing the correlated host with impurities, we discuss the ground state properties as a function of magnetic field H and the Kondo exchange coupling. While an isolated impurity of spin S>1/2 has a magnetic ground state of effective spin (S−12), a finite concentration introduces a heavy impurity band and yields a singlet ground state with antiferromagnetically correlated impurities. A field H first polarizes the narrow impurity band. The impurities have mixed valent properties induced in part by correlations in the host. Some aspects of the model are related to heavy fermion alloys.
We review analytical and numerical results derived from the Bethe ansatz solution of the n-channel Kondo model of arbitrary spin S as a function of temperature, external field, impurity spin S and the number of channels n. Three situations have to be distinguished: (i) If n = 2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n < 2S the impurity spin is only partially compensated (undercompensated), and (iii) if n > 2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are discussed in the context of magnetic impurities, e.g. Fe, Cr and Tm in simple metals, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian Heisenberg model and electron assisted-tunnelling of an atom in a double-well potential.