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.
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.
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.
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 investigate a transverse-field Ising chain with dimerized anisotropic Gamma interactions and demonstrate that, both in the absence and presence of Ising interactions, the competition between Gamma anisotropy and the transverse field gives rise to vector chiral order and dynamical quantum phase transitions. The phase diagram comprises positive and negative vector chiral phases and a paramagnetic phase, characterized by the vector spin chirality and the vector chiral order parameter. In the absence of Ising interactions, we identify a gapless critical line that exhibits no finite-size drift, along which the spin-spin correlations and subsystem entanglement entropy display behavior distinct from that of Ising criticality. Furthermore, we find that the critical times of dynamical quantum phase transitions form periodic or aperiodic sequences, depending on the quench path. Our findings highlight how dimerized off-diagonal exchange enriches both equilibrium ordering and dynamical critical behavior in a quantum Ising chain.
We investigate the effect of non-Hermitian Gamma interaction on the phase transitions and magnetic correlations for the transverse field Ising chain. We demonstrate that apart from the gapped antiferromagnetic and paramagnetic phases, there is a gapless phase induced by parity-time symmetry breaking, where the system exhibits long-range and short-range spin-nematic correlations in different regions divided by the quantum critical line determined from the correlation function and the subsystem entanglement entropy. Furthermore, we reveal that the parity-time symmetry breaking leads to the emergence of dynamical spin-nematic correlation, which also suggests a way of characterizing the spin-nematic map through non-equilibrium dynamics. Our findings show rich quantum phases stem from the competition among the Ising interaction, transverse field and non-Hermitian Gamma interaction, as well as providing a scheme for generating spin-nematic correlation in the spin chain.
We investigate the spin-1/2 XX chain with uniform Gamma interaction under a transverse magnetic field. By exactly diagonalizing the Hamiltonian using the Fermionization technique, we rigorously analyze the energy spectrum, distinguishing between gapped and gapless domains at absolute zero. Additionally, we thoroughly examine various order parameters, including magnetization, staggered magnetization, chirality, and spin nematicity, which delineate the diverse phases within the ground state phase diagram, each characterized by its unique long-range order. Notably, we identify a hybrid critical line in the ground state phase diagram. This hybrid critical line is defined as a line where multiple types of phase transitions converge. At points along this line, the system exhibits behaviors characteristic of different types of critical points simultaneously. Understanding the magnetic properties under different field conditions can lead to the development of new magnetic materials and technologies. Our results provide a framework for experimentally manipulating magnetic fields, allowing researchers to control and observe changes in material properties. This, in turn, offers valuable insights into the fundamental physics governing these systems.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudo-spin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudo-spin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse field only emerges at zero field and is of the second-order. Several critical exponents obtained by finite size scaling analysis are the same as those in the 1D transverse field Ising model, suggesting the same universality class. A logarithmic divergence of the entanglement entropy of a block at the quantum critical point is also observed. From the calculated coefficient connected to the central charge of the conformal field theory, it is suggested that the block entanglement depends crucially on the detailed topological structure of a system.