Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2012-04-22
Physics
Condensed Matter
Strongly Correlated Electrons
6 pages, 7 figures, 1 table
Scientific paper
In strongly correlated systems, numerical algorithms taking parity quantum numbers into account are not only used to accelerate computation by reducing dimension of Hilbert space, but also needed by some manipulations like the Level Spectroscopy (LS) method. By comparing energy difference between different parity quantum numbers, the LS method is an important technique in identifying quantum critical points of Gaussian and Berezinsky-Kosterlitz-Thouless (BKT) type quantum phase transitions. These transitions occurring in many one-dimensional systems are usually difficult to be studied numerically. Although the LS method is a good strategy to locate critical points, it has been lacked an algorithm which is able to deal with large size systems with parity quantum numbers for the past years. 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 about the existence of an intermediate phase in the present model is the first time supported by DMRG.
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