The determination of the ground-state energy of an antiferromagnetic lattice by means of a renormalization procedure

Abstract

An approximate value for the ground-state energy of an antiferromagnetic lattice of spins one-half is determined by means of a repeated renormalization procedure in which the lattice is divided into cells with an effective interaction. This effective interaction is determined on the basis of the spin-hamiltonian formalism.

An exact limit for the Peierls distortion energy in an antiferromagnetic chain by means of a renormalization procedure

“…For this case, however, a far better approximation was given in a previous paper. (8) Our results for sco given in Fig. 3 and Table I Pytte (5~ has analyzed the Peierls distortion for a linear antiferromagnetic chain in interaction with three-dimensional phonons.…”

“…8, we divide the spin system into cells of three spins (i = 3k -1, 3k, 3k + 1) and the energy eigenvalues for these cells are …”

Exact value of the ground state energy of the linear antiferromagnetic Heisenberg chain with nearest and next-nearest neighbour interactions

“…Let the E(7)~-~. (5) lowest eigenvalue of HN(7) be EN (7). We are interested This shows that E(7) takes its maximal value~at in the energy per spin in the ground state in the limit =~if we show that E(~)= -~.…”

“…( -1.7726, ..,). For 7*0 only approximations and upper and lower bounds for E (7) are knwon [3][4][5][6][7][8].…”

On the ground state energy of the linear antiferromagnetic Heisenberg chain with nearest- and next-nearest-neighbour interactions

“…Approximations for general y have been given by Ono (1972), Ananthakrishna et al(1976), van de Braak et al (1977) and van den Broek et a1 (1980). Upper bounds have been given by Majumdar and Ghosh (1969a), Niemeyer (1971), van de Braak et a1 (1977,1979) and van den Broek et a1 (1980).…”