Twist Method for Quantum Ground-State Problems and its Application to Antiferromagnetic Heisenberg Chains with Competing Interactions

Abstract

We present a quantum version of the twist method which has been developed for classical systems. A finite size scaling form for the excess ground state energy is derived and tested for an S=1/2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions: H= J ∑ (S_j · S_j+1 +α S_j · S_j+2 )with J>0 and α >0. Using an exact diagonalization method, we obtain the critical value α_c ≅ 0.246 of the fluid-dimer transition, which is very close to the reliable value recently obtained by Okamoto and Nomura (Phys. Lett. A 169 (1992) 433).