Magnetization Plateau of theS= 1/2 Frustrated Heisenberg Chain with Period 3 Parity Invariant Exchange Modulation

Abstract

The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate ↑↑↓-type plateau states in the uniform chain, two of them (↓↑↑↓↑↑... and ↑↓↑↑↓↑... ) turned out to be robust against the period 3 exchange modulation which favors the ○-○ ↑○-○ ↑... phase up to a critical value of the modulation amplitude (○-○ = singlet dimer) resulting in the Z 2 symmetry broken phase. Another ↑↑↓-type state with ↑↑↓↑↑↓... configuration is stabilized for period 3 modulation with opposite sign. The transition between the ○-○↑ ○-○ ↑...-phase and Z 2 -broken phase is the Ising transition and that between the ↑↑↓↑↑↓... -phase and Z 2 broken phase is the first. order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.