Parity quantum numbers in the density matrix renormalization group

Abstract

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.

Edge Modes in the Intermediate-D and Large-D Phases of the S = 2 Quantum Spin Chain with XXZ and On-Site Anisotropies

“…Very similar situations are found in the S = 1 chain with the on-site anisotropy and the bond alternation [12], and in the S = 1 two-leg ladder [13]. Slightly after our works [3][4][5], Tzeng [14] confirmed our results by use of the density matrix renormalization group (DMRG) and the LS analysis. He used the parity DMRG because the classification of the eigenstates by the parity is essential for the LS analysis of the numerical data.…”

Ground-State Phase Diagram of an Anisotropic S = 1 Ferromagnetic–Antiferromagnetic Bond-Alternating Chain

“…2j,2j+1 are split into three levels with T z = 0, T z = ±1 and T z = ±2. We note that this effect is expressed as theD 2 (T z j ) 2 andD 4 (T z j ) 4 terms in the effective Hamiltonian (12). For our parameter set (β = −0.2 and D 2 = −1/30), these energies are…”

Long-range magnetic order and interchain interactions in theS=2chain systemMnCl3(bpy)

“…Magnetic chains composed of spin S = 2 ions have received considerable theoretical and numerical attention [1][2][3][4][5][6][7][8] due to their unique predicted behavior. Even-and odd-integer spin chains are distinct, with the latter in a symmetry-protected topological phase [3,9].…”