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arXiv:cond-mat/9710229 · Journal of the Physical Society of Japan

Magnetic and Critical Properties of Alternating Spin Heisenberg Chain in a Magnetic Field

Tetsuji Kuramoto

Published May 15, 1998• 43 citations
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Abstract

We study magnetic and critical properties of the alternating spin antiferromagnetic Heisenberg chain with $S=1/2$ and 1 in a magnetic field at T=0. The numerical diagonalization is applied to the system up to $2N=20$ sites. Checking numerically that magnetic states with the magnetization per site $m$ obey a conformal field theory with conformal anomaly $c=1$ for $1/4

DOI
10.1143/jpsj.67.1762

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We study magnetic and critical properties of the alternating spin antiferromagnetic Heisenberg chain with S=1/2S=1/2S=1/2 and 1 in a magnetic field at T=0. The numerical diagonalization is applied to the system up to 2N=202N=202N=20 sites. Checking numerically that magnetic states with the magnetization per site mmm obey a conformal field theory with conformal anomaly c=1c=1c=1 for $1/4
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The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centres are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centred in the mixed Heisenberg chain where we have at even (odd) sites a spin- SU(2) operator interacting with a XXZ-like interaction (anisotropy ). Our results indicate universal properties for all these chains. The whole phase, , where the models change from ferromagnetic to ferrimagnetic behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions.
The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S ′) SU(2) operator interacting with a XXZ like interaction (anisotropy ∆). Our results indicate universal properties for all these chains. The whole phase, 1> ∆> −1, where the models change from ferromagnetic ( ∆ = 1) to ferrimagnetic ( ∆ = −1) behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions. 1
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}.