Improved finite-lattice method for estimating the zero-temperature properties of two-dimensional lattice models

Abstract

The well-known finite-lattice method for the calculation of the properties of quantum spin systems on a two-dimensional lattice at zero temperature was introduced in 1978. The method has now been greatly improved for the square lattice by including finite lattices based on parallelogram tiles as well as the familiar finite lattices based on square tiles. Dozens of these new finite lattices have been tested and graded using the [Formula: see text] ferromagnet. In the process new and improved estimates have been obtained for the XY model's ground-state energy per spin, ε0 = −0.549 36(30) and spontaneous magnetization per spin, m = 0.4349(10). Other properties such as near-neighbour, zero-temperature spin–spin correlations, which appear not to have been calculated previously, have been estimated to high precision. Applications of the improved finite-lattice method to other models can readily be carried out.

Numerical studies of photon-based spectroscopies on high- superconductors

“…To obtain a bandstructure suitable for the cuprates, we also include a next-nearest-neighbor hopping t i, j σ c † iσ c jσ [11]. We focus on the 4, 8, and 16B Betts clusters [10] with PBC depicted in Fig. 1(b).…”

Possible phase separation in square and honeycomb Hubbard model: A variational cluster study

“…However, full diagonalization is still possible within relatively small Hubbard clusters such as squares, 8-site 2 × 4 ladders, two-dimensional Betts cells and pyramids [34,35]. The problem of a quantum gas of interacting many electrons in independent clusters is exactly solvable in the ground state and at finite temperatures [13][14][15][16][17].…”

Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets

“…(Extrapolation of the DMRG results in the infinite-lattice limit yields ε g = −0.3321J). The best available dressed cluster method (DCM) [42], coupled cluster method (CCM) [43] and real-space renormalization group with effective interactions (RSRG-EI) [44] These estimates should be compared with the known results -0.1116 and 0.0637, correspondingly [45].…”