Renormalization techniques for quantum spin systems. Ground-state energies

Abstract

Introduction and general outline of the method 225 3. Examples. Ising and isotropic XY systems with a transverse 2. Examples. Systems without external magnetic field 229 magnetic field 251 2.1. Linear chain with nearest and next-nearest neighbour 4. Concluding remarks 256 interactions; first order 230 Appendix A: Algebraic properties of the spin 257 2.2. Peierls-distorted chain 232 Appendix B: Kramers' theorem 259 2.3. Triangular lattice 238 Appendix C: The Wigner-Eckart theorem 261 2.4. Linear chain; variational method 240 References 262 2.5. Linear chain; second order 244

Statistical mechanics and the physics of many-particle model systems

“…The question of the true antiferromagnetic ground state is not completely clarified up to the present time. [272][273][274][275][276] This is related to the fact that, in contrast to ferromagnets, which have a unique ground state, antiferromagnets can have several different optimal states with the lowest energy. The Neel ground state is understood as a possible form of the system's wave function, describing the antiferromagnetic ordering of all spins.…”

Ground-state energies of antiferromagnetic lattices

“…For the Hamiltonian of this system we refer to ref. 6, in which the same normalization is used as in this work, i.e. the interaction between nearest neighbours is represented by 45i" $~+1, whereas the ratio of the interaction constants for next-nearest neighbours and nearest neighbours is represented by 3/.…”

“…The values of ~(y) as a function of y on the basis of our calculations are shown in table VII. A simple similarity transformation of the Hamiltonian (6) in which H is replaced by U+HU shows that ~(y) is an even function of y. For U one should take://I(2S~) in which//~ represents the product for all spins of one sublattice.…”