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/0002184 · Physical review. B, Condensed matter

Magnetic impurities in a one-dimensional spin-orbital model

Yu-Wen Lee, Yu-Li Lee

Published Aug 1, 2000• 0 citations
arXivHTMLPDF

Abstract

Using a one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low-energy dynamics in the gapless phase through bosonization and renormalization-group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid-like corrections to thermodynamical quantities (except the possible Curie-like contributions from the residual moments in the former cases). In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional Heisenberg spin chain and multiband Hubbard models is also made.

DOI
10.1103/physrevb.62.3279

Related papers

Quantum phase transitions in models of coupled magnetic impurities

Matthias Vojta C, R. Bulla, Walter Hofstetter

We discuss models of interacting magnetic impurities coupled to a metallic host, which show one or more boundary quantum phase transitions where the ground-state spin changes as a function of the interimpurity couplings. The simplest example is realized by two spin-$\frac{1}{2}$ Kondo impurities coupled to a single orbital of the host. We investigate the phase diagram and crossover behavior of this model and present numerical renormalization-group results together with general arguments showing that the singlet-doublet quantum phase transition is either of first order or of the Kosterlitz-Thouless type, depending on the symmetry of the Kondo couplings. Thus we find an exponentially small energy scale within the Kondo regime, and a two-stage Kondo effect, in a single-channel situation. Connections to other models and possible applications are discussed.

arXiv:cond-mat/0106458•Physical review. B, Condensed matter•Apr 1, 2002•122 citations

Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths

Serge Florens, Lars Fritz, Matthias Vojta C

We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of ${Z}_{2}$ frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow flow toward a stable strong-coupling state. Since the low-energy bosons exist around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.

arXiv:cond-mat/0703609•Physical Review B•Jun 15, 2007•9 citations

Kondo effect in XXZ spin chains

Akira Furusaki, Takashi Hikihara

The Kondo effect in a one-dimensional spin-$\frac{1}{2}$ $\mathrm{XXZ}$ model in the gapless $\mathrm{XY}$ regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin $(S=1/2)$ is coupled to a single spin in the $\mathrm{XXZ}$ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host $\mathrm{XXZ}$ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host $\mathrm{XXZ}$ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.

arXiv:cond-mat/9802258•Physical review. B, Condensed matter•Sep 1, 1998•25 citations

Phase Diagram of an Impurity in the Spin- 1/2 Chain: Two-Channel Kondo Effect versus Curie Law

Sebastian Eggert, David Gustafsson, Stefan Rommer

We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J1 and the coupling between the two sites J2. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a nontrivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi-liquid fixed point with a logarithmically diverging impurity susceptibility as in the two-channel Kondo effect. Our results resolve a controversy about the renormalization flow.

arXiv:cond-mat/0011001•Physical Review Letters•Jan 15, 2001•19 citations

BOUNDARY POTENTIAL EFFECT FOR THE KONDO PROBLEM IN A LUTTINGER LIQUID: INTEGRABLE CASE

Yupeng Wang, Duo Jin, Fu‐Cho Pu

To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we introduce a model of ferromagnetic single-impurity Kondo problem in a multi-band one-dimensional δ-potential Fermi gas, which is exactly solvable for a special Kondo coupling constant via Bethe ansatz. It is found that the boundary potential modifies the local moment seriously due to the charge-spin coupling and the strong backward scattering off the impurity, and thus strongly affects the fixed point of the system. Generally, their is a residual entropy for the ground state which depends on the strength of the boundary potential. In addition, the tunneling effect through the impurity and the breakdown of the open boundary induced by the impurity are also discussed.

International Journal of Modern Physics B•Mar 10, 1999•0 citations

Magnetic impurity coupled to a Heisenberg chain: Density-matrix renormalization-group study

W. Zhang, J. Igarashi, Peter Fulde

By making use of the Lanczos and the density-matrix renormalization-group methods, we study the zero-temperature properties of a spin-1/2 antiferromagnetic Heisenberg chain system with a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins. A comparison is made with the results for a magnetic impurity coupled only to the nearest-neighbor spin in the chain. The binding energy and the spin correlations are calculated. The matrix elements of the impurity spin operators are also calculated between several low-energy states. By carefully analyzing finite-size effects, we show that the dynamical structure factor of the impurity contains a \ensuremath{\delta}-function contribution at zero frequency which does not vanish in the thermodynamic limit for the case of symmetrical coupling. This indicates a partial decoupling of the impurity spin from the spins in the chain, and therefore the impurity susceptibility is predicted to show a Curie behavior. This contradicts the two-channel Kondo behavior suggested from analytic considerations.

Physical review. B, Condensed matter•Jul 1, 1997•24 citations
Using a one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low-energy dynamics in the gapless phase through bosonization and renormalization-group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid-like corrections to thermodynamical quantities (except the possible Curie-like contributions from the residual moments in the former cases). In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional Heisenberg spin chain and multiband Hubbard models is also made.
We discuss models of interacting magnetic impurities coupled to a metallic host, which show one or more boundary quantum phase transitions where the ground-state spin changes as a function of the interimpurity couplings. The simplest example is realized by two spin-12\frac{1}{2}21​ Kondo impurities coupled to a single orbital of the host. We investigate the phase diagram and crossover behavior of this model and present numerical renormalization-group results together with general arguments showing that the singlet-doublet quantum phase transition is either of first order or of the Kosterlitz-Thouless type, depending on the symmetry of the Kondo couplings. Thus we find an exponentially small energy scale within the Kondo regime, and a two-stage Kondo effect, in a single-channel situation. Connections to other models and possible applications are discussed.
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2{Z}_{2}Z2​ frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow flow toward a stable strong-coupling state. Since the low-energy bosons exist around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.
The Kondo effect in a one-dimensional spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ model in the gapless XY\mathrm{XY}XY regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin (S=1/2)(S=1/2)(S=1/2) is coupled to a single spin in the XXZ\mathrm{XXZ}XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ\mathrm{XXZ}XXZ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host XXZ\mathrm{XXZ}XXZ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.
We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J1 and the coupling between the two sites J2. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a nontrivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi-liquid fixed point with a logarithmically diverging impurity susceptibility as in the two-channel Kondo effect. Our results resolve a controversy about the renormalization flow.
To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we introduce a model of ferromagnetic single-impurity Kondo problem in a multi-band one-dimensional δ-potential Fermi gas, which is exactly solvable for a special Kondo coupling constant via Bethe ansatz. It is found that the boundary potential modifies the local moment seriously due to the charge-spin coupling and the strong backward scattering off the impurity, and thus strongly affects the fixed point of the system. Generally, their is a residual entropy for the ground state which depends on the strength of the boundary potential. In addition, the tunneling effect through the impurity and the breakdown of the open boundary induced by the impurity are also discussed.
By making use of the Lanczos and the density-matrix renormalization-group methods, we study the zero-temperature properties of a spin-1/2 antiferromagnetic Heisenberg chain system with a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins. A comparison is made with the results for a magnetic impurity coupled only to the nearest-neighbor spin in the chain. The binding energy and the spin correlations are calculated. The matrix elements of the impurity spin operators are also calculated between several low-energy states. By carefully analyzing finite-size effects, we show that the dynamical structure factor of the impurity contains a \ensuremath{\delta}-function contribution at zero frequency which does not vanish in the thermodynamic limit for the case of symmetrical coupling. This indicates a partial decoupling of the impurity spin from the spins in the chain, and therefore the impurity susceptibility is predicted to show a Curie behavior. This contradicts the two-channel Kondo behavior suggested from analytic considerations.