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

Physical review. B, Condensed matter

Closing of the spin gap and ferromagnetism induced by magnetic impurities

P. Schlottmann

Published May 1, 1998• 4 citations
Publisher

Abstract

The Hubbard chain with attractive $U$ and a finite concentration of magnetic impurities of spin $S$ is studied using the Bethe Ansatz technique. The impurities weaken the singlet bound states of the Hubbard model reducing the spin gap. The spin gap is closed at a critical concentration which depends on the spin and the coupling strength. A ferromagnetic phase is induced for concentrations of impurities larger than the critical one, where a fraction of singlet pairs is broken up giving rise to a Fermi sea of spin-polarized itinerant electrons.

DOI
10.1103/physrevb.57.10638

Related papers

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

Closing of a spin gap and ferromagnetism induced by magnetic impurities: finite-size effects and critical exponents

P. Schlottmann, Andrei A. Zvyagin

We consider the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.

Journal of Physics Condensed Matter•Nov 28, 2000•2 citations

Magnetic impurities coupled to quantum antiferromagnets in one dimension

J. Igarashi, Takashi Tonegawa, Makoto Kaburagi +1 more

Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.

arXiv:cond-mat/9412104•Physical review. B, Condensed matter•Mar 1, 1995•54 citations

Hubbard chain with a Kondo impurity

P.-A. Bares, K Grzegorczyk

A Bethe ansatz solution of a (modified) Hubbard chain with a Kondo impurity of arbitrary spin S at a highly symmetric line of parameter space is proposed and explored. Our results confirm the existence of a strong-coupling (line of) fixed-point(s) with ferromagnetic Kondo coupling as first hypothetized by Furusaki and Nagaosa on the basis of perturbative renormalization group calculations. For on-site Hubbard repulsion and ferromagnetic Kondo exchange, the ground state has spin S − 1/2, i.e. , is a singlet when S = 1/2. The contributions of the impurity to the magnetic susceptibility and low-temperature specific heat are discussed. While the Wilson ratio is unity in the half-filled band, it is found to be a function of density and interaction away from half-filling.

arXiv:cond-mat/9810310•Europhysics Letters (EPL)•Apr 1, 1999•5 citations

Heisenberg spin chain with many impurities

P. Schlottmann

We consider the Heisenberg chain of spin 1/2 with a concentration x of impurity spins S. The thermodynamic Bethe ansatz equations are stated for this model. The ground-state equations are analyzed as a function of x and magnetic field. In zero field the ground state is a singlet for finite x, but non-Fermi-liquid-like for x\ensuremath{\rightarrow}0. Two energy bands play a role at T=0. The Van Hove singularities of the empty bands define two critical fields, ${\mathit{H}}_{\mathit{c}1}$(x) and ${\mathit{H}}_{\mathit{c}2}$(x), at which the susceptibility diverges. The non-Fermi-liquid behavior as x\ensuremath{\rightarrow}0 arises from nonanalyticities as ${\mathit{H}}_{\mathit{c}2}$ vanishes.

Physical review. B, Condensed matter•Apr 1, 1994•36 citations

Ferromagnetic Quantum critical behavior in three-dimensional Hubbard model with transverse anisotropy

Naoum Karchev

One-band Hubbard model with transverse anisotropy is considered at density of electrons $n=0.4$. It is shown that when the anisotropy is appropriately chosen, the ground state is ferromagnetic with magnetic order perpendicular to the anisotropy. The increasing of the ratio $\frac tU$, where $t$ is the hopping parameter and $U$ is the Coulomb repulsion, decreases the Curie temperature, and the system arrives at the quantum critical point $(T_C=0)$. The result is obtained introducing Schwinger bosons and slave Fermions representation of the electron operators. Integrating out the spin-singlet Fermi fields an effective Heisenberg model with ferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Owing to the anisotropy, the magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.

arXiv:1207.1674•Jul 6, 2012•0 citations
The Hubbard chain with attractive UUU and a finite concentration of magnetic impurities of spin SSS is studied using the Bethe Ansatz technique. The impurities weaken the singlet bound states of the Hubbard model reducing the spin gap. The spin gap is closed at a critical concentration which depends on the spin and the coupling strength. A ferromagnetic phase is induced for concentrations of impurities larger than the critical one, where a fraction of singlet pairs is broken up giving rise to a Fermi sea of spin-polarized itinerant electrons.
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 the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.
Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.
A Bethe ansatz solution of a (modified) Hubbard chain with a Kondo impurity of arbitrary spin S at a highly symmetric line of parameter space is proposed and explored. Our results confirm the existence of a strong-coupling (line of) fixed-point(s) with ferromagnetic Kondo coupling as first hypothetized by Furusaki and Nagaosa on the basis of perturbative renormalization group calculations. For on-site Hubbard repulsion and ferromagnetic Kondo exchange, the ground state has spin S − 1/2, i.e. , is a singlet when S = 1/2. The contributions of the impurity to the magnetic susceptibility and low-temperature specific heat are discussed. While the Wilson ratio is unity in the half-filled band, it is found to be a function of density and interaction away from half-filling.
We consider the Heisenberg chain of spin 1/2 with a concentration x of impurity spins S. The thermodynamic Bethe ansatz equations are stated for this model. The ground-state equations are analyzed as a function of x and magnetic field. In zero field the ground state is a singlet for finite x, but non-Fermi-liquid-like for x\ensuremath{\rightarrow}0. Two energy bands play a role at T=0. The Van Hove singularities of the empty bands define two critical fields, Hc1{\mathit{H}}_{\mathit{c}1}Hc1​(x) and Hc2{\mathit{H}}_{\mathit{c}2}Hc2​(x), at which the susceptibility diverges. The non-Fermi-liquid behavior as x\ensuremath{\rightarrow}0 arises from nonanalyticities as Hc2{\mathit{H}}_{\mathit{c}2}Hc2​ vanishes.
One-band Hubbard model with transverse anisotropy is considered at density of electrons n=0.4n=0.4n=0.4. It is shown that when the anisotropy is appropriately chosen, the ground state is ferromagnetic with magnetic order perpendicular to the anisotropy. The increasing of the ratio tU\frac tUUt​, where ttt is the hopping parameter and UUU is the Coulomb repulsion, decreases the Curie temperature, and the system arrives at the quantum critical point (TC=0)(T_C=0)(TC​=0). The result is obtained introducing Schwinger bosons and slave Fermions representation of the electron operators. Integrating out the spin-singlet Fermi fields an effective Heisenberg model with ferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Owing to the anisotropy, the magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.