Kiyohide Nomura

Fluid-dimer critical point in S = 12 antiferromagnetic Heisenberg chain with next nearest neighbor interactions

Abstract We numerically investigate the critical value αc of the fluid-dimer transition in the ground state of the S = 1 2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions, H = JΣ (Sj·Sj+1+αSj·Sj+2) with J > 0 and α > 0. With the help of the conformal field theory, we can estimate αc = 0.2411 ± 0.0001.

Critical properties of S= 1/2 antiferromagnetic XXZ chain with next-nearest-neighbour interactions

We investigate numerically the critical lines and the critical properties of the fluid-dimer and the Neel-dimer transitions of the S= 1/2 antiferromagnetic XXZ chain with next-nearest interactions, and we confirm that the universality class of this model belongs to the quantum sine-Gordon model, as is expected from the bosonization. The method which we use in this paper to calculate the critical lines is free from the logarithmic corrections on the Kosterlitz-Thouless (K-T)-type transition line, which have made the K-T critical point difficult to obtain. By the use of this method, it is possible to determine the K-T critical line with high precision from small size data, and to identify the universality class.

Phase Diagram of S =1⁄2 Antiferromagnetic XXZ Chain with Next-Nearest-Neighbor Interactions

We numerically investigate the critical lines of the fluid-dimer and the Neel-dimer transitions of the S=1/2 antiferromagnetic XXZ chain with next-nearest interactions, assuming the asymptotic behavior to be determined by the quantum sine-Gordon model. Our result is different from that of Tonegawa, Harada and Kaburagi, who used the phenomenological renormalization group (PRG). We show that the PRG may lead to a false critical point when it is applied to the Kosterlitz-Thouless-type transitionWe numerically investigate the critical lines of the fluid-dimer and the Neel-dimer transitions of the S =1/2 antiferromagnetic XXZ chain with next-nearest interactions, assuming the asymptotic behavior to be determined by the quantum sine-Gordon model. Our result is different from that of Tonegawa, Harada and Kaburagi, who used the phenomenological renormalization group (PRG). We show that the PRG may lead to a false critical point when it is applied to the Kosterlitz-Thouless-type transition.

Critical Properties of S = 1 Bond-Alternating XXZ Chains and Hidden Z2 x Z2 Symmetry

Critical properties of the spin-1 bond-alternating XXZ chain are studied numerically. This model is appropriate to study the VBS picture and hidden Z 2 × Z 2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the X Y , the Haldane, the dimer, and the Neel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z 2 × Z 2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Neel and dimer-Neel). We determine the phase boundary and universality class using the recent developed techniques by the authors.

A new phase of the S=1 bilinear-biquadratic chain : a trimerized state

We investigate the S =1 bilinear-biquadratic model. In some region, the trimerized variational state is a good candidate for the ground state. This explains why the Sutherland model ( J 1 >0 and J 2 / J 1 =-1) has soft modes at q =0, ±2π/3. Moreover, the full phase diagram of this model is discussed. It is found that at the pure biquadratic ferromagnetic point, the ground state is extremely degenerate.

Critical properties of the XXZ chain in an external staggered magnetic field

We comment on the recent work of Alcaraz and Malvezzi on the critical properties of the chain in staggered magnetic field. The method of determining the phase boundary from the finite-size numerical data is also discussed.

Phase Transitions of S = 3/2 and S = 2 XXZ Spin Chains with Bond Alternation

Based on the universality concept, we study the S =3/2 and S =2 bond-alternating spin chains numerically. In previous papers, the phase diagram of the S =1 XXZ spin chain with bond alternation was shown to reflect the hidden Z 2 × Z 2 symmetry. For the higher S Heisenberg spin chain, the successive dimerization transition occurs, and for anisotropic spin chains the phase structure will be more colorful than the S =1 case. Using recently developed techniques, we show directly that the phase structure of the anisotropic spin chains relates to the Z 2 × Z 2 symmetry.

Phase separation as an instability of the Tomonaga-Luttinger liquid

Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional

Phase diagram of S = 1 bond-alternating XXZ chains

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Logarithmic corrections of the one-dimensional S=1/2 Heisenberg antiferromagnet.

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