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Physical review. B, Condensed matter

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

Steven P. Strong, Andrew J. Millis

Published Oct 1, 1994• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.50.9911

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We study the behavior of a model of two XXZ spin chains coupled by an isotropic exchange interaction JK{\mathit{J}}_{\mathit{K}}JK​ as the anisotropies and spin velocities in the individual chains are varied. In the limit of large antiferromagnetic JK{\mathit{J}}_{\mathit{K}}JK​ we map the model's low-energy sector onto an Ising model in a transverse field; in the limit of large ferromagnetic JK{\mathit{J}}_{\mathit{K}}JK​ we map the model's low-energy sector onto that of a single spin-one chain. For small JK{\mathit{J}}_{\mathit{K}}JK​, 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.
The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent \ensuremath{\beta}=8/(1+ \ensuremath{\surd}7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.
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Exact low-temperature asymptotic behavior of boundary contribution to specific heat and susceptibility in the one-dimensional spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ model with exchange anisotropy $1/2<\ensuremath{\Delta}<~1$ is analytically obtained using the Abelian bosonization method. The boundary spin susceptibility is divergent in the low-temperature limit. This singular behavior is caused by the first-order contribution of a bulk leading irrelevant operator to boundary free energy. The result is confirmed by numerical simulations of finite-size systems. The anomalous boundary contributions in the spin isotropic case are universal.