Frustration-Induced Gaplessness in the Frustrated Transverse Ising Ring

New effects in the frustrated transverse Ising ring are predicted. The system is solved based on a mapping of Pauli spin operators to the Jordan-Wigner fermions. We group the low-lying energy levels into bands after imposing appropriate parity constraint, which projects out the redundant degrees of freedom brought about by the Jordan-Wigner fermions. In the region of strong antiferromagnetic coupling, we uncover an unusual gapless phase induced by the ring frustration. We demonstrate that its ground state exhibits a strong longitudinal spin-spin correlation and possesses a considerably large entropy of entanglement. The low-lying energy levels evolve adiabatically in the gapless phase, which facilitates us to work out new behaviors of density of states, low-temperature correlation functions and specific heat. We also propose an experimental protocol for observing this peculiar gapless phase.