Physical Review Letters

Competition between singlet formation and magnetic ordering in one-dimensional spin systems

Steven P. Strong, Andrew J. Millis

Published Oct 19, 1992• 136 citations

Abstract

We use mappings onto soluble models and Abelian bosonization to determine the phase diagram and correlation functions of a model of two coupled spin chains. We find quantum disordered singlet phases and magnetic phases and determine the phase boundaries, universality classes of transitions, and correlation functions. We believe our model captures the essential physics of the interplay between the Kondo effect and magnetic ordering, which may be important for the heavy fermion materials.

DOI: 10.1103/physrevlett.69.2419

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Physical Review Letters

Competition between singlet formation and magnetic ordering in one-dimensional spin systems

Steven P. Strong, Andrew J. Millis

Published Oct 19, 1992• 136 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.69.2419

Related papers

Competition between singlet formation and magnetic ordering in one-dimensional spin systems

Steven P. Strong, Andrew J. Millis

We study the behavior of a model of two XXZ spin chains coupled by an isotropic exchange interaction ${\mathit{J}}_{\mathit{K}}$ as the anisotropies and spin velocities in the individual chains are varied. In the limit of large antiferromagnetic ${\mathit{J}}_{\mathit{K}}$ we map the model's low-energy sector onto an Ising model in a transverse field; in the limit of large ferromagnetic ${\mathit{J}}_{\mathit{K}}$ we map the model's low-energy sector onto that of a single spin-one chain. For small ${\mathit{J}}_{\mathit{K}}$ , we study the model perturbatively via Abelian and non-Abelian bosonization. We determine the possible phases, approximate locations of the phase boundaries, universality classes of the transitions, and asymptotic behavior of correlation functions. We believe our model captures the essential physics of the interplay between the compensation of local moments and magnetic ordering, which may be important for the heavy-fermion materials.We study the behavior of a model of two XXZ spin chains coupled by an isotropic exchange interaction ${\mathit{J}}_{\mathit{K}}$ as the anisotropies and spin velocities in the individual chains are varied. In the limit of large antiferromagnetic ${\mathit{J}}_{\mathit{K}}$ we map the model's low-energy sector onto an Ising model in a transverse field; in the limit of large ferromagnetic ${\mathit{J}}_{\mathit{K}}$ we map the model's low-energy sector onto that of a single spin-one chain. For small ${\mathit{J}}_{\mathit{K}}$, we study the model perturbatively via Abelian and non-Abelian bosonization. We determine the possible phases, approximate locations of the phase boundaries, universality classes of the transitions, and asymptotic behavior of correlation functions. We believe our model captures the essential physics of the interplay between the compensation of local moments and magnetic ordering, which may be important for the heavy-fermion materials.

Physical review. B, Condensed matterOct 1, 199457 citations

Localized spin ordering in Kondo lattice models

Ian P. McCulloch, Aušrius Juozapavičius, Anders Rosengren +1 more

Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.

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Spin gaps in two models of strongly correlated electron systems

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Magnetic order and strongly correlated effects in the one-dimensional Ising-Kondo lattice

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arXiv:2401.00432Physical review. B./Physical review. BMay 3, 20244 citations

Quantum phase transition of Ising-coupled Kondo impurities

Markus Garst, Stefan K. Kehrein, Thomas Pruschke +2 more

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization-group arguments, we show that at this transition the conductance $G$ through the system either displays a zero-bias anomaly, $G\ensuremath{\sim}{\ensuremath{\mid}V\ensuremath{\mid}}^{\ensuremath{-}2(\sqrt{2}\ensuremath{-}1)}$, or takes a universal value, $G=({e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}){\mathrm{cos}}^{2}(\ensuremath{\pi}∕2\sqrt{2})$, depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows us to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization-group calculations. In the singlet phase close to the quantum phase transition, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic minidomain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow-equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization-group arguments, we show that at this transition the conductance $G$ through the system either displays a zero-bias anomaly, $G\ensuremath{\sim}{\ensuremath{\mid}V\ensuremath{\mid}}^{\ensuremath{-}2(\sqrt{2}\ensuremath{-}1)}$, or takes a universal value, $G=({e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}){\mathrm{cos}}^{2}(\ensuremath{\pi}∕2\sqrt{2})$, depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows us to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization-group calculations. In the singlet phase close to the quantum phase transition, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic minidomain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow-equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.

arXiv:cond-mat/0310222Physical Review BJun 18, 200452 citations

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.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/0106458Physical review. B, Condensed matterApr 1, 2002122 citations

We study the behavior of a model of two XXZ spin chains coupled by an isotropic exchange interaction

{\mathit{J}}_{\mathit{K}}

as the anisotropies and spin velocities in the individual chains are varied. In the limit of large antiferromagnetic

{\mathit{J}}_{\mathit{K}}

we map the model's low-energy sector onto an Ising model in a transverse field; in the limit of large ferromagnetic

{\mathit{J}}_{\mathit{K}}

we map the model's low-energy sector onto that of a single spin-one chain. For small

{\mathit{J}}_{\mathit{K}}

, we study the model perturbatively via Abelian and non-Abelian bosonization. We determine the possible phases, approximate locations of the phase boundaries, universality classes of the transitions, and asymptotic behavior of correlation functions. We believe our model captures the essential physics of the interplay between the compensation of local moments and magnetic ordering, which may be important for the heavy-fermion materials.

G

through the system either displays a zero-bias anomaly, $G\ensuremath{\sim}{\ensuremath{\mid}V\ensuremath{\mid}}^{\ensuremath{-}2(\sqrt{2}\ensuremath{-}1)}$, or takes a universal value, $G=({e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}){\mathrm{cos}}^{2}(\ensuremath{\pi}∕2\sqrt{2})$, depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows us to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization-group calculations. In the singlet phase close to the quantum phase transition, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic minidomain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow-equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.

\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.