arXiv subjects
Publications and source records attributed to Atsuhiro Kitazawa.
Berezinskii-Kosterlitz-Thouless (BKT) transition is one of the instability mechanisms for the Tomonaga-Luttinger liquid. But in the BKT transition, there are logarithmic-correction problems, which make it very difficult to treat BKT transitions numerically. We propose a method, ``level spectroscopy'', to overcome such difficulties, based on the renormalization group analysis and the symmetry consideration.
We study the breakdown of the magnetization plateau at the magnetization M=M_{S}/3 (M_{S} is the saturation magnetization) of the S=1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J_{F}, and anisotropic antiferromagnetic coupling (J_{x}=J_{y}=J_{AF} and J_{z}=ΔJ_{AF}). For the limit of large γ\equiv J_{F}/J_{AF}, the model is equivalent to the S=3/2 XXZ chain with the exchange anisotropy Δ. There is a phase transition between the plateau (small-γ) and the no-plateau (large-γ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For Δ=1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point γ_{c}=15.4.
We reexamine the numerical study of the magnetized state of the S=3/2 spin chain with single ion anisotropy D(> 0) for the magnetization M=M_{S}/3, where M_{S} is the saturation magnetization. We find at this magnetization that for D D_{c1}, the parameter region is divided into two parts D_{c1} < D < D_{c2}=0.943 and D_{c2} < D. In each region, the system is gapful and the M=M_{S}/3 magnetization plateau appears in the magnetization process. From our numerical calculation, the intermediate region D_{c1} < D < D_{c2} should be characterized by a magnetized valence-bond-solid state.
We study the magnetization plateau at a third of the saturation magnetization of the S=1/2 trimerized XXZ spin chain at T=0. The appearance of the plateau depends on the values of the XXZ anisotropy and the magnitude of the trimerization. This plateauful-plateauless transition is a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type, which is difficult to precisely detect from the numerical data. To determine the phase boundary line of this transition precisely, we use the level crossing of low-lying excitations obtained from the numerical diagonalization. We also discuss the S=1/2 ferromagnetic-ferromagnetic-antiferromagnetic chain.
We give the details of the analysis for critical properties of spin-gap phases in one-dimensional lattice electron models. In the Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is shown to be equivalent to that of the level-crossing of the singlet and the triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the t-J model, and the t-J-J' model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.
We study the S=1 quantum spin chains with bilinear, biquadratic, plus bond alternation in the vicinity of the S=1 Takhtajan-Babujian model. Transition line between the Haldane and the dimer phases are determined numerically. To see the crossover behavior from c=3/2 (k=2 SU(2) WZW model) at the Takhtajan-Babujian point to c=1 (k=1 SU(2) WZW model), we calculate the conformal anomaly c and scaling dimensions of the primary fields on the transition line.
We study the plateau of the magnetization curve at $M = M_{\rm s}/3$ ($M_{\rm s}$ is the saturation magnetization) of the $S=1/2$ trimerized $XXZ$ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the $Δ-t$ plane, where $Δ$ denotes the $XXZ$ anisotropy and $t$ the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.
Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D sine-Gordon model, plays an important role in the low dimensional physics. We relate the operator content of the BKT transition to that of the SU(2) Wess-Zumino-Witten model, using twisted boundary conditions. With this method, in order to determine the BKT critical point, we can use the level crossing of the lower excitations than the periodic boundary case, thus the convergence to the transition point is highly improved. Then we verify the efficiency of this method by applying to the S=1,2 spin chains.
We study the spin-gap phase in the one-dimensional t-J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also check that the universality class of the transition belongs to the $k=1$ SU(2) Wess-Zumino-Witten model.
We study the phase diagram of S=3/2 and S=2 bond-alternating spin chains numerically. In previous papers, the phase diagram of S=1 XXZ spin chain with bond-alternation was shown to reflect the hidden $Z_{2}\times Z_{2}$ symmetry. But 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 methods, we show directly that the phase structure of the anisotropic spin chains relates to the $Z_{2}\times Z_{2}$ symmetry.
The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Néel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times 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-Néel and dimer-Néel). We determine the phase boundary and universality class using the recent developed techniques by the authors.
It was a difficult problem to determine the Gaussian fixed line from the numerical data, because close to the Berezinskii-Kosterlitz-Thouless multicritical point the divergence of the correlation length becomes very slow. Considering the renormalization group behavior, we find an efficient method to determine the Gaussian fixed line.
The phase transitions between the XY, the dimer and the Haldane phases of the spin-1 bond-alternating XXZ chain are studied by the numerical diagonalization. We determine the phase diagram at $T=0$ and also identify the universality class with the level spectroscopy. We find that exactly on $Δ=0$ there is a Berezinskii-Kosterlitz-Thouless transition line which separates the XY and the Haldane phase and there exists a multicritical point of the XY, the dimer and the Haldane phases. We discuss that the critical properties of this model is of the 2-D Ashkin-Teller type reflecting the hidden $Z_2\times Z_2$ symmetry.