Quantum Phase Transition Induced by Geometrical Changes in Spin–Phonon Interaction

Abstract

Spin–phonon interaction effects in a spin-1/2 antiferromagnetic Heisenberg chain coupled to phonons are investigated in systems with variable crystal structures. By performing a unitary transformation to a Hamiltonian of the system, we derive effective Hamiltonians expanded in powers of spin–phonon and spin–spin couplings. Ground-state phase transitions between a spin-liquid phase and a spin-gapped phase are investigated by a level spectroscopy analysis of numerical diagonalization data of effective systems. Our results depend on whether the ground state of the Heisenberg chain is in the spin-liquid phase or the spin-gapped phase. In the system where the ground state is in the spin-liquid phase, the spin–phonon interaction causes the usual phase transition to the spin-gapped phase. On the other hand, in the system where the ground state is in the spin-gapped phase, the spin–phonon interaction causes the novel phase transition to the spin-liquid phase for some geometrical structures. The phase transition f...