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arXiv:cond-mat/0204174 · Physical review. B, Condensed matter

Phase diagram and critical properties of the frustrated Kondo necklace model in a magnetic field

Takahiro Yamamoto, Kôichirô Ide, Chikara Ishii

Published Sep 9, 2002• 9 citations
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Abstract

The critical properties of the frustrated Kondo necklace model with a half saturation magnetization $(m=1/2)$ have been studied by means of an exact-diagonalization method. It is shown from bosonization technique that the model can be effectively expressed as a quantum sine-Gordon model. Thus it may show three (dimer plateau, N\'eel plateau and Tomonaga-Luttinger liquid) phases due to competitions among the Ising anisotropy $\ensuremath{\Delta},$ and the nearest- and next-nearest-neighbor exchange interactions ${J}_{1}$ and ${J}_{2}.$ The boundary lines on the $\ensuremath{\Delta}$-${J}_{2}{/J}_{1}$ phase diagram separating the three phases are determined by the method of level spectroscopy, based on the conformal field theory.

DOI
10.1103/physrevb.66.104408

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The critical properties of the frustrated Kondo necklace model with a half saturation magnetization (m=1/2)(m=1/2)(m=1/2) have been studied by means of an exact-diagonalization method. It is shown from bosonization technique that the model can be effectively expressed as a quantum sine-Gordon model. Thus it may show three (dimer plateau, N'eel plateau and Tomonaga-Luttinger liquid) phases due to competitions among the Ising anisotropy \ensuremathΔ,\ensuremath{\Delta},\ensuremathΔ, and the nearest- and next-nearest-neighbor exchange interactions J1{J}_{1}J1​ and J2.{J}_{2}.J2​. The boundary lines on the \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ-J2/J1{J}_{2}{/J}_{1}J2​/J1​ phase diagram separating the three phases are determined by the method of level spectroscopy, based on the conformal field theory.
The magnetization plateaus of frustrated Kondo necklace model have been studied with use of the bosonization technique and level spectroscopy method. It is shown that the model may show three phases (dimer plateau, Néel plateau and Tomonaga-Luttinger liquid phases) due to competitions among Ising anisotropy Δ, the nearest and next nearest neighbor exchange interactions J1, J2. It is shown from bosonization technique that quantum transition between the dimer and Néel plateaus is Gaussian type, while the transition from one of these plateau phases to Tomonaga-Luttinger phase is Brezinskii-Kosterlitz-Thouless type. The phase diagram is constructed on the Δ-J2/J1 plane with use of level spectroscopy method, under the condition that the system has a half of the saturation magnetization.
The magnetization process of one-dimensional Kondo necklace model with next-nearest-neighbor interaction has been studied by the use of exact-diagonalization method. The magnetization plateaus appear at zero ( m =0) and at half ( m =1/2) of the saturation magnetization. The ground state in the absence of a magnetic field is regarded as an aggregate of intra-atomic Kondo singlets. On the other hand, the spin configuration at the 1/2-plateau represents the intra-chain dimer (σ-dimer) phase with broken translational symmetry. The picture for spin configurations in the uniform magnetic fields other than m =0 and 1/2 are also given. We also determined the phase diagram for the ground state of the system in the magnetic field.
We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-12\frac{1}{2}21​ Luttinger liquid coupled by a Kondo exchange interaction JK{J}_{K}JK​ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling J1{J}_{1}J1​ and a next-nearest-neighbor (frustrating) exchange interaction J2{J}_{2}J2​. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling JK{J}_{K}JK​ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios JK/J1{J}_{K}/{J}_{1}JK​/J1​, J2/J1{J}_{2}/{J}_{1}J2​/J1​, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.
We study the one-dimensional spin-12\frac{1}{2}21​ Heisenberg model with antiferromagnetic nearest-neighbor J1{J}_{1}J1​ and next-nearest-neighbor J2{J}_{2}J2​ exchange couplings in magnetic field hhh. With varying dimensionless parameters J2/J1{J}_{2}/{J}_{1}J2​/J1​ and h/J1h/{J}_{1}h/J1​, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave (SDW2)({\text{SDW}}_{2})(SDW2​), and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, SDW2{\text{SDW}}_{2}SDW2​, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge c=1+1c=1+1c=1+1), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.
We present a comprehensive computational study of the phase diagram of the frustrated S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2)({J}_{2})(J2​) and third-neighbor (J3)({J}_{3})(J3​) couplings. Using a combination of exact diagonalizations (EDs) of the original spin model, of the Hamiltonian projected into the nearest-neighbor short-range valence-bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence-bond crystal phase. At larger J2{J}_{2}J2​, we locate a sizable region in which staggered valence-bond crystal correlations are found to be important, either due to genuine valence-bond crystal (VBC) ordering or as a consequence of magnetically ordered phases, which break lattice rotational symmetry. Furthermore, we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior---such as a deconfined critical point---across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half filled Hubbard model on the honeycomb lattice.
In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz-Thouless transition from a gapful phase to a gapless spin liquid phase.