Quantum ising model with staggered interaction

A. Benyoussef, T. Biaz, M. Touzani

Mohammad Reza Soltani, Javad Vahedi, Alireza Sadremomtaz +1 more

Geoffrey Grimmett

Dongchang Liu, Su Yao, Xia Jin +2 more

The quantum criticality and entanglement properties are investigated in the one-dimensional spin-1/2 transverse field Ising model with staggered Dzyaloshinsky-Moriya interaction by utilizing the infinite-time evolving block decimation method. In this model, the staggered Dzyaloshinsky-Moriya interaction does not lead any new phase, while it only appears a phase transition line between Néel phase and paramagnetic phase. The behaviors of measurements of information illustrate the quantum phase transition and the existence of factorized points. The factorization phenomena is observed in the transverse Néel phase detecting by the entanglement quantities, in which the double degenerate ground state in transverse Néel phase is preserved by the Dzyaloshinsky-Moriya interaction also evidencing from the fidelity map. From the perspective of magnetism, the existence of chiral order and transverse Néel order suggests the helical magnetic structure induced by Dzyaloshinsky-Moriya interaction. The critical exponents and central charge keep invariant and convinced that the phase transitions belong to the Ising universality class. In contrary to the systems confined within central charge c=1, although the competition between the Dzyaloshinsky-Moriya interaction and external field changes the phase transition and entanglement properties, the quantum criticality seems independent of Dzyaloshinsky-Moriya interaction.

Ai Min Chen, Dongchang Liu, Xia Jin +2 more

Abstract This study investigates the quantum phase transitions and critical behaviors in the transverse Ising model with staggered Γ interaction by utilizing the infinite-time evolving block decimation method in the infinite matrix product states representation. The ground-state phase diagram shows that the system exhibits a phase transition from the transverse Néel phase to the paramagnetic phase as the transverse magnetic field increases, which are characterized by the local magnetization and non-local transverse Néel order. The chiral order and nematic order are calculated to explore the helical and nematic magnetic structure caused by the Γ interaction. From the spin-spin correlation, a modulated commensurate power-law oscillating decay behavior provides insight in analyzing the ground state characteristics of each phase. In order to study the quantum criticality, the critical exponents β , ν and central charge c are extracted and numerically consistent with the Ising class transition, demonstrating that the critical behavior in our model occurs is independent of the emergent Gamma interaction.

Geoffrey Grimmett