Parity quantum numbers in the density matrix renormalization group

In strongly correlated systems, numerical algorithms taking parity quantum numbers into account are used not only for accelerating computation by reducing the Hilbert space but also for particular manipulations such as the level spectroscopy (LS) method. By comparing energy differences among different parity quantum numbers, the LS method is a crucial technique used in identifying quantum critical points of Gaussian and Berezinsky-Kosterlitz-Thouless- (BKT) type quantum phase transitions. These transitions that occur in many one-dimensional systems are usually difficult to study numerically. Although the LS method is an effective strategy to locate critical points, it has lacked an algorithm that can manage large systems with parity quantum numbers. Here a parity density matrix renormalization group (DMRG) algorithm is discussed. The LS method is used with the DMRG in the S = 2 XXZ spin chain with uniaxial anisotropy. Quantum critical points of BKT and Gaussian transitions can be located well. Thus, the LS method becomes a very powerful tool for BKT and Gaussian transitions. In addition, Oshikawa's hypothesis in 1992 on the presence of an intermediate phase in the present model is supported by DMRG.