Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1801.10509 · Physical review. B./Physical review. B

Heisenberg spin- 12 XXZ chain in the presence of electric and magnetic fields

Pradeep K. Thakur, P. Durganandini

Published Feb 20, 2018• 14 citations
arXivHTMLPDF

Abstract

We study the interplay of electric and magnetic order in the one-dimensional Heisenberg spin-$\frac{1}{2}$ 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.

DOI
10.1103/physrevb.97.064413

Related papers

Magnetic phase diagram of a spin-1/2 X X Z chain with modulated Dzyaloshinskii-Moriya interaction

G. I. Japaridze, Hadi Cheraghi, S. Mahdavifar

We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.

arXiv:2106.15714•Physical review. E•Jul 26, 2021•15 citations

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

Yang‐Hao Chan, Wen Jin, Hong‐Chen Jiang +1 more

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic $XXZ$ spin-$1/2$ Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid, one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [I. Garate and I. Affleck, Phys. Rev. B 81, 144419 (2010)]. We also confirm the prevalence of the ${N}^{z}$ N\'eel Ising order in the regime of comparable DM and magnetic field magnitudes.

arXiv:1708.03670•Physical review. B./Physical review. B•Dec 29, 2017•23 citations

Field-induced ordered phases in anisotropic spin- 1 2 Kitaev chains

Mandev Bhullar, Haoting Xu, Hae‐Young Kee

Motivated by intense research on two-dimensional spin-$\frac{1}{2}$ Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one-dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.

arXiv:2501.03329•Physical review. B./Physical review. B•Mar 31, 2025•3 citations

Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction

Tian-Cheng Yi, Wen‐Long You, Ning Wu +1 more

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.

arXiv:1907.05303•Physical review. B./Physical review. B•Jul 23, 2019•68 citations

Factorization, coherence, and asymmetry in the Heisenberg spin- 12 XXZ chain with Dzyaloshinskii-Moriya interaction in transverse magnetic field

Pradeep K. Thakur, P. Durganandini

We investigate the factorization, coherence, and asymmetry properties of the one-dimensional Heisenberg spin-$\frac{1}{2}$ 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 ${h}_{\text{pf}}$. 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.

arXiv:2008.06097•Physical review. B./Physical review. B•Aug 12, 2020•18 citations

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains*

Yuchen Fan, Rong Yu

In quasi-one-dimensional (q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic (AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations, and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave (LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.

Chinese Physics B•Mar 23, 2020•5 citations
We study the interplay of electric and magnetic order in the one-dimensional Heisenberg spin-12\frac{1}{2}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.
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.
We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZXXZXXZ spin-1/21/21/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid, one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [I. Garate and I. Affleck, Phys. Rev. B 81, 144419 (2010)]. We also confirm the prevalence of the Nz{N}^{z}Nz N\'eel Ising order in the regime of comparable DM and magnetic field magnitudes.
Motivated by intense research on two-dimensional spin-12\frac{1}{2}21​ Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one-dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.
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-12\frac{1}{2}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)U(1)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)U(1)U(1) symmetry is minimal. Our calculations indicate a phase coherent ground state at hpf{h}_{\text{pf}}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 zzz 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.
In quasi-one-dimensional (q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic (AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations, and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave (LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.