In this work, we address the ground-state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases---antiferromagnetic, paramagnetic, and chiral---and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.
In this work, we address the ground-state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases---antiferromagnetic, paramagnetic, and chiral---and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.
We investigate the factorization, coherence, and asymmetry properties of the one-dimensional Heisenberg spin-21 XXZ chain with Dzyaloshinskii-Moriya interaction (DMI) and a transverse magnetic field using quantum information measures. Both longitudinal and transverse DM vectors are considered. Using numerical DMRG methods, we compute bipartite entanglement estimators like the one-tangle, two-spin concurrence and quantum coherence estimators like the Wigner-Yanase-skew information. We show that a longitudinal DMI destroys the factorizability property while a transverse DMI preserves it. We relate the absence of factorizability to the breaking of the U(1) rotation symmetry about the local magnetization axis at each lattice site. Physically, the breaking of the symmetry manifests in the existence of a chiral current. Furthermore, we show that although the longitudinal DMI destroys the factorization property, there is a ``pseudofactorizing'' field at which the entanglement and hence violation of the U(1) symmetry is minimal. Our calculations indicate a phase coherent ground state at hpf. An entanglement transition (ET) occurs across this field which is characterized by an enhanced but finite range of two-spin concurrence in its vicinity in contrast with the diverging range of the concurrence for the ET across the factorizing field. We relate the asymmetry to the ``frameness'' or the ability for the state to act as a reference frame for some measurement. In the absence of the longitudinal DMI (or in the presence of a transverse DMI), at the factorizing field, the single site magnetization axis serves to specify the common z axis for the full system but not the full Cartesian reference frame due to a lack of phase reference. On the other hand, in the presence of a longitudinal DMI, our results indicate that at the pseudofactorizing field, the local magnetization and the chiral current are sufficient to specify the full Cartesian reference frame with the chiral current serving as the macroscopic quantity to determine the phase reference.
We study the interplay of electric and magnetic order in the one-dimensional Heisenberg spin-21 XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (DM) interaction and with longitudinal and transverse magnetic fields, interpreting the DM interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped N\'eel phase with antiferromagnetic (AF) order, gapped saturated phase, and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the N\'eel phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.
The effects of the Dzyaloshinski—Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ∊ k of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log 2 L ( L is the length of a subchain) with the coefficient A ≈ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ = 0 and 0 < h ≤ 1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.
In this paper, we study the quantum coherence of one-dimensional transverse XY model with Dzyaloshinskii-Moriya interaction, which is given by the following Hamiltonian:HXY=∑i=1N((1+γ/2) σixσi+1x+(1-γ/2) σiyσi+1y-hσiz) ∑i=1ND(σixσi+1y-σiyσi+1x).(8)Here, 0 ≤ γ ≤ 1 is the anisotropic parameter, h is the magnitude of the transverse magnetic field, D is the strength of Dzyaloshinskii-Moriya (DM) interaction along the z direction. The limiting cases such as γ=0 and 1 reduce to the isotropic XX model and the Ising model, respectively. We use the Jordan-Winger transform to map explicitly spin operators into spinless fermion operators, and then adopt the discrete Fourier transform and the Bogoliubov transform to solve the Hamiltonian Eq.(8) analytically. When the DM interactions appear, the excitation spectrum becomes asymmetric in the momentum space and is not always positive, and thus a gapless chiral phase is induced. Based on the exact solutions, three phases are identified by varying the parameters:antiferromagnetic phase, paramagnetic phase, and gapless chiral phase. The antiferromagnetic phase is characterized by the dominant x-component nearest correlation function, while the paramagnetic phase can be characterized by the z component of spin correlation function. The two-site correlation functions Grxy and Gryx (r is the distance between two sites) are nonvanishing in the gapless chiral phase, and they act as good order parameters to identify this phase. The critical lines correspond to h=1, γ=2D, and h=√4D2 -γ2 + 1 for γ>0. When γ=0, there is no antiferromagnetic phase. We also find that the correlation functions undergo a rapid change across the quantum critical points, which can be pinpointed by the first-order derivative. In addition, Grxy decreases oscillatingly with the increase of distance r. The correlation function Grxy for γ=0 oscillates more dramatically than for γ=1. The upper boundary of the envelope is approximated as Grxy~r-1/2, and the lower boundary is approximately Grxy~r-3/2, so the long-range order is absent in the gapless chiral phase. Besides, we study various quantum coherence measures to quantify the quantum correlations of Eq.(8). One finds that the relative entropy CRE and the Jensen-Shannon entropy CJS are able to capture the quantum phase transitions, and quantum critical points are readily discriminated by their first derivative. We conclude that both quantum coherence measures can well signify the second-order quantum phase transitions. Moreover, we also point out a few differences in deriving the correlation functions and the associated density matrix in systems with broken reflection symmetry.
Abstract The quantum phase transition (QPT) and quantum criticality of an anisotropic spin-1/2 XY chain under the interplay of magnetic field and Dzyaloshinskii–Moriya (DM) interaction, which is interpreted as an electric field, are investigated, wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order. It is shown that the thermal Drude weight is a good quantity to characterize the gapped ( D th = 0) and gapless ( D th > 0) ground states. The continuous QPT is marked by a quantum critical point (QCP) associated with entropy accumulation, which is manifested by a characteristic Güneisen ratio (GR) with or without self-duality symmetry. It is shown that at a self-dual QCP, the GR keeps a finite value as T → 0, while at a general QCP without self-duality symmetry, it displays a power-law temperature dependent divergence: Γ( T , r c ) ∼± T −1 , which provides a novel thermodynamic means for probing QPT.
We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with uniform and alternating transverse magnetic fields (ATXY) in the presence of the Dzyaloshinskii-Moriya (DM) interaction by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field (UXY), which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show the appearance of a new gapless chiral phase---in the XY model with uniform as well as alternating field. We further observe that first derivatives of nearest neighbor two-site entanglement with respect to magnetic fields can detect all the critical lines present in the system. We also find that the factorization surface at zero temperature present in this model without DM interaction becomes a volume on the introduction of the latter. Moreover, DM interaction turns out to be good to generate bipartite entanglement sustainable at large times, leading to a proof of ergodic nature of bipartite entanglement in this system.