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Journal of Magnetism and Magnetic Materials

Characterizing quantum criticality in the transverse field Ising model with staggered Dzyaloshinskii–Moriya interaction

Dongchang Liu, Su Yao, Xia Jin, Zhijie Zhao, Ai Min Chen

Published Dec 22, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1016/j.jmmm.2023.171659

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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.
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.
We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.
The one-dimensional spin-1/2 XXZ model with the limited case of the staggered Gamma interaction which includes the staggered DM and KSEA interactions is investigated by utilizing the infinite-time evolving block decimation method in the infinite matrix product state representation. It is shown that the staggered DM interaction does not lead to any new phase but expands the XY phase. Contrasted to the DM interaction, the region of the ferromagnetic phase expands into the nematic-ferromagnetic and dimer-Haldane phases with the deconfined quantum phase transition happening in the case of KSEA interaction. We observe a pronounced effect in the entanglement entropy and Schmidt gap, the odd-bond and even-bond von Neumann entropies exhibit different values, and the value of the Schmidt gap on the even bond becomes zero in the dimer-Haldane phase. This implies that quantum entanglement and the Schmidt gap can distinguish the two degenerate ground states caused by the existence of dimerized interaction. The zero value of the Schmidt gap works as a sign of the topological phase, which is also evidenced by the string correlation. From the perspective of magnetism, the existence of chiral order and nematic order suggests the helical magnetic structure induced by Gamma interaction. By comparing the DM and KSEA interactions, it is found that DM interaction does not change ferromagnetism, whereas the KSEA interaction inhibits ferromagnetism and destroys the product state in the ferromagnetic phase. Furthermore, the behaviors of the spin structure factor for the transversal spin correlation can distinguish different phases. From an appropriate fitting exponent of the spin correlation oscillating decay, commensurate or incommensurate phases can be identified.
We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and Néel phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.
We consider a class of one-dimensional compass models with staggered Dzyaloshinskii-Moriya exchange interactions in an external transverse magnetic field. Based on the exact solution derived from Jordan-Wigner approach, we study the excitation gap, energy spectra, spin correlations and critical properties at phase transitions. We explore mutual effects of the staggered Dzyaloshinskii-Moriya interaction and the magnetic field on the energy spectra and the ground-state phase diagram. Thermodynamic quantities including the entropy and the specific heat are discussed, and their universal scalings at low temperature are demonstrated.
We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.