科研之友
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摘要
String correlations are investigated in an infinite-size XXZ spin-1 chain. By using the infinite matrix product state representation, we calculate a long-range string order directly rather than an extrapolated string order in a finite-size system. In the Neel phase, the string correlations decay exponentially. In the XY phase (Tomonaga-Luttinger liquid phase), the behavior of the string correlations shows a unique two-step decaying to zero within a relatively very large lattice distance for any finite truncation dimension but its disappearance with zero string correlation in the thermodynamic limit, which makes a finite-size study difficult to verify the non-existence of the string order. Thus, in the Haldane phase, the non-vanishing string correlations in the limit of a very large distance allow to characterize the phase boundaries to the XY phase and the Neel phase, which implies that the transverse long-range string order is the order parameter for the Haldane phase. In addition, the singular behavior of the von Neumann entropy and the fidelity per lattice site is shown to capture clearly the phase transition points that are consistent with the results from the transverse long-range string order. The estimated critical points including a Berezinsky-Kosterlitz-Thouless transition from the XY phase to the Haldane phase agree well with the previous results: Delta(c2) = 0 for the XY-Haldane phase transition and Delta(c3) = 1.185 for the Haldane-Neel phase transition from the density renormalization group. From a finite-entanglement scaling of the von Neumann entropy with respect to the truncation dimension, the central charges are found to be c similar or equal to 1.0 at Delta(c2) = 0 and c similar or equal to 0.5 at Delta(c3) = 1.185, respectively, which shows that the XY-Haldane phase transition at Delta(c2) = 0 belongs to the Heisenberg universality class, while the Haldane-Neel phase transition at Delta(c2) = 1.185 belongs to the two-dimensional classical Ising universality class. It is also shown that, the long-range order parameters and the von Neumann entropy, as well as the fidelity per site approach, can be applied to characterize quantum phase transitions as a universal phase transition indicator for one-dimensional lattice many-body systems.
- 出版日期2012-7
- 单位重庆大学
