Quantum Phase Transition of S=1/2 Trimerized XXZ Spin Chain in Magnetic Field

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.Comment: LaTeX2e, 4 pages, 2eps figures, submitted to conference on Strongly Correlated Electron System

SU(2)/Z2SU(2)/Z_2 symmetry of the BKT transition and twisted boundary conditio n

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.Comment: LaTex2e,, 33 pages, 14 figures in eps file

Phase diagram of S=1/2 two-leg XXZ spin ladder systems

We investigate the ground state phase diagram of the S=1/2 two-leg $XXZ$ spin ladder system with an isotropic interchain coupling. In this model, there is the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-Haldane and the XY-rung singlet phase boundaries. It was difficult to determine the transition line using traditional methods. We overcome this difficulty using the level spectroscopy method combined with the twisted boundary condition method, and we check the consistency. We find out that the phase boundary between XY phase and Haldane phase lies on the $\Delta=0$ line. And we show that there exist two different XY phases, which we can distinguish investigating a $XX$ correlation function

Magnetization-plateau state of the S=3/2 spin chain with single ion anisotropy

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}=0.387 the system is critical and the magnetization plateau does not appear. 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.Comment: 6 pages, 8 figure

Bifurcation at the c=3/2 Takhtajan-Babujian point to the c=1 critical lines

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.Comment: 10 pages, 8 figure

Renormalization group analysis of the spin-gap phase in the one-dimensional t-J model

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.Comment: 4 pages(RevTeX), 5 figures(EPS), TITCMT-97-10, to appear in Phys. Rev. Let

Spin-Gap Phases in Tomonaga-Luttinger Liquids

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.Comment: 14 pages(REVTeX), 9 figures(EPS), 1 table, To appear in PRB, Detailed paper of PRL 79 (1997) 3214 and JPSJ 67 (1998) 71