  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 difference between 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 been lacked an algorithm that can manage large systems
with parity quantum numbers. Here a new parity Density Matrix Renormalization
Group (DMRG) algorithm is discussed. The LS method is the first time performed
by 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 conjecture in 1992 on the presence of an intermediate phase in the
present model is the first time supported by DMRG.
