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arXiv:cond-mat/9611026 · Journal of the Physical Society of Japan

Magnetic and Critical Properties of Alternating Spin Chain withS=1/2, 1in Magnetic Fields

Mitsuru Fujii, Satoshi Fujimoto, Norio Kawakami

Published Aug 15, 1996• 21 citations
arXivHTMLPDF

Abstract

We study an integrable spin chain with an alternating array of spins S=1/2, 1 in external magnetic fields using the Bethe ansatz exact solution. The calculated magnetization possesses a cusp structure at a critical magnetic field H=H_{C}, at which the specific heat shows a divergence property. We also calculate finite-size corrections to the energy spectrum, and obtain the critical exponents of correlation functions with the use of conformal field theory (CFT). Low-energy properties of the model are described by two c=1 U(1) CFTs in HH_{C}.

DOI
10.1143/jpsj.65.2381

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We study an integrable spin chain with an alternating array of spins S=1/2, 1 in external magnetic fields using the Bethe ansatz exact solution. The calculated magnetization possesses a cusp structure at a critical magnetic field H=H_{C}, at which the specific heat shows a divergence property. We also calculate finite-size corrections to the energy spectrum, and obtain the critical exponents of correlation functions with the use of conformal field theory (CFT). Low-energy properties of the model are described by two c=1 U(1) CFTs in HH_{C}.
The spectral properties and phase diagram of the exact integrable spin one quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated to an unknown R-matrix whose dependence on the spectral parameters is not of difference form. The associated Bethe ansatz equations, that fix the eigenspectra, are distinct from those associated to other known integrable spin models. The model has a free parameter tpt_ptp​. We show that at the special point tp=1t_p=1tp​=1 the model gets an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q=exp⁡(i2π/3)q=\exp(i2π/3)q=exp(i2π/3) andin the presence of an external magnetic field. Our analysis is done either by solving the associated Bethe-ansatz equations or by direct diagonalization of thequantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by c=1c=1c=1 conformal field theory separated from a massive phase by first-order phase transitions.
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The quantum periodic XXZ chain with alternating spins is studied. The properties of the related R-matrix and Hamiltonians are discussed. A compact expression for the ground state energy is obtained. The corresponding conformal anomaly is found via the finite-size computations and also by means of the Bethe ansatz method. In the presence of an external magnetic field, the magnetic susceptibility is derived. The results are also generalized to the case of a chain containing several different spins.
We investigate the low-temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the model in a weak magnetic field is derived with the help of Wiener-Hopf techniques. It turns out that the low-energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(2)\text{SU}(2)SU(2) Heisenberg spin chain. However, these two types of conformally invariant low-lying excitations may break down as excitations take place far away from the Fermi points. The long distance asymptotics of the correlation functions and the critical exponents for the model in the presence of a magnetic field at zero temperature are derived in detail by solving dressed charge equations and by conformal mapping. Furthermore, we calculate the conformal dimensions for particular cases of correlation functions. The leading terms of these correlation functions are given explicitly for a weak magnetic field $H\ensuremath{\ll}1$ and for a magnetic field close to the critical field $H\ensuremath{\rightarrow}{H}_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.
In this thesis the low temperature properties of an exactly solvable anti-ferromagnetic spin S = 1 chain doped with mobile spin S = 1 =2 impurities will be considered.The doped spin S = 1 chain is a generalization of the super-symmetric t-J model and interpolates between the isotropic spin S = 1 =2 HEISENBERG model and the spin S = 1 TAKHTAJAN-BABUJIAN chain for the completely doped case and vanishing impurity concentration x h = 0 respectively.Within the framework of the Quantum Inverse Scattering Method the doped spin S = 1 chain can be built from a gl(2j1)-invariant solution of the graded YANG-BAXTER equation corresponding to the atypical [1] + -representation of the super-algebra gl(2j1).The associated transfer matrix is diagonalized by means of a nested algebraic BETHE ansatz.Using a generalized fusion procedure the Hamiltonian and it's eigenvalues are constructed.By applying TAKAHASHI's string hypothesis we deduce in the third part the thermodynamic BETHE ansatz equations.Performing the low temperature limit we can determine ground state properties and the phase diagram depending on an external magnetic field H and the impurity concentration x h .The system shows spin-charge separation.We also examine the magnetic properties of the model.For sufficiently high magnetic fields and finite impurity concentration we find a new metallic phase with a finite gap for the magnetic excitations.In this phase the magnetization curve shows a plateau that is only a fraction of the saturation magnetization and can be tuned by the impurity concentration x h .The critical behavior near the edges of the plateau is also analyzed.To study the dynamical properties e.g. the low lying magnetic excitations we calculate the Finite Size Correction of the model.Using predictions of Conformal Field Theory we can identify the effective low temperature theories as well as the scaling dimensions which determine the asymptotic behavior of the correlation functions at criticality.In the plateau phase no magnetic excitations are found to exist.