Takashi Tonegawa, Toshiya Hikihara, Kiyomi Okamoto, Shunsukc C. Furuya, Toru Sakai
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 87(10) 104002-1-104002-11, Oct, 2018 Peer-reviewed
We explore the ground-state phase diagram of the S = 1/2 two-leg ladder with different leg interactions. The xy- and z-components of the leg interactions between nearest-neighbor spins in the a (b) leg are respectively denoted by J(1,a) and Delta(1)J(1,a )(J(1,b) and Delta(1)J(1,b)). On the other hand, the xy- and z-components of the uniform rung interactions are respectively denoted by Gamma(r)J(r) and J(r). In the above, Delta(1) and Gamma(r) are the XXZ-type anisotropy parameters for the leg and rung interactions, respectively. This system has frustration when J(1,a) J(1,b) < 0 irrespective of the sign of J(r). The phase diagram on the Delta(1)(vertical bar Delta(1)vertical bar <= 1.0) versus J(1,b) ( -2 . 0 <= J(1,b), <= 3.0) plane in the case where J(1,a) = 0.2, J(r) = -1.0, and Gamma(r) = 0.5 is determined numerically. We employ physical considerations and perform level spectroscopy and phenomenological renormalization-group analyses of the numerical data obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, Neel, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and XY1 phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated region. We perform first-order perturbational calculations from the strong-rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we carry out density-matrix renormalizationgroup calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram. The phase diagram on the Gamma(r) (0.0 <= Gamma(r <=) 1.0) versus J(1,b) (-1.0 <= J(1,b) <= 2.0) plane in the case where J(1,a), = 0.2, J(r) = -1.0, and Delta(1) = 1.0 is also discussed briefly.