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:2209.04102 · Physical review. B./Physical review. B

Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction

E. S. Ma, K. L. Zhang, Z. Song

Published Dec 15, 2022• 12 citations
arXivHTMLPDF

Abstract

We systematically investigate possible helix states in the XXZ Heisenberg model with the Dzyaloshinskii-Moriya (DM) interaction. Exact solutions show that a set of precession helix states can be constructed by deliberate superposition of degenerate eigenstates of the Hamiltonian under the resonant condition. When a non-Hermitian balance boundary term is imposed as a quenching action, the quench dynamics shows that a steady helix state emerges from some easily prepared initial states, including saturated and maximally mixed ferromagnetic states, according to the analysis of the perturbation method. The corresponding dynamics for near resonant cases is also investigated numerically, indicating the robustness of the scheme. Our findings highlight the cooperation of non-Hermiticity and the DM interaction in a quantum spin system, suggesting a way for preparing a steady helix state in a non-Hermitian quantum spin system.

DOI
10.1103/physrevb.106.245122

Related papers

Generalized spin helix states in quantum spin graphs

C.H. Zhang, Youguo Shi, Z. Song

Abstract In general, the summation of a set of sub-Hamiltonians cannot share a common eigenstate of each one, only if it is an unentangled product state, such as a spin helix state in quantum spin system. Here we present a method, referred to as the building block method (BBM), for constructing possible spin-1/2 XXZ Heisenberg lattice systems possessing spin helix states. We focus on two types of XXZ dimers as basic elements, with a non-Hermitian parity-time ( P T ) magnetic field and Hermitian Dzyaloshinskii-Moriya interaction (DMI), which share the same degenerate eigenstates. Based on these two building blocks, one can construct a variety of Heisenberg quantum spin systems, which support helix states with zero energy. Furthermore, we show that such systems act as quantum spin graphs since they obey the analogs of Kirchhoff’s laws for sets of spin helix states when the non-Hermitian P T terms cancel each other out. In addition, the dynamic response of the helix states for three types of perturbations is also investigated analytically and numerically. Our findings provide a way to study quantum spin systems on irregular lattices.

Physica Scripta•Jan 28, 2025•1 citation

Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction

Youguo Shi, Z. Song

Phantom helix states are a special set of degenerate eigenstates of the XXZ Heisenberg model which lie in the energy levels around zero energy and are bidirectionally equal. In this work, we study the helix state in the XXZ Heisenberg model with the Dzyaloshinskii-Moriya interaction (DMI). We show exactly that only the helix states in one direction remain unchanged in the presence of resonant DMI. Based on the Holstein-Primakoff transformation, the quantum spin model is mapped to a boson model, which allows us to understand the underlying mechanism. Furthermore, it also indicates that such phantom states can be separated from the spectrum by the strong DMI to enhance the robustness of the states. We demonstrate the dynamic formation processes of unidirectional phantom helix states by numerical simulations. The results indicate that the DMI, as expected, acts as a filter with high efficiency.

arXiv:2306.11578•Physical review. B./Physical review. B•Aug 4, 2023•5 citations

Generalized phantom helix states in quantum spin graphs

Chunsu Zhang, Youguo Shi, Z. Song

In general, the summation of a set of sub-Hamiltonians cannot share a common eigenstate of each one, only if it is an unentangled product state, such as a phantom helix state in quantum spin system. Here we present a method, referred to as the building block method (BBM), for constructing possible spin-1/2 XXZ Heisenberg lattice systems possessing phantom helix states. We focus on two types of XXZ dimers as basic elements, with a non-Hermitian parity-time (PT ) field and Hermitian Dzyaloshinskii-Moriya interaction (DMI), which share the same degenerate eigenstates. Based on these two building blocks, one can construct a variety of Heisenberg quantum spin systems, which support helix states with zero energy. The underlying mechanism is the existence of a set of degenerate eigenstates. Furthermore, we show that such systems act as quantum spin graphs since they obey the analogs of Kirchhoff's laws for sets of spin helix states when the non-Hermitian PT fields cancel each other out. In addition, the dynamic response of the helix states for three types of perturbations is also investigated analytically and numerically. Our findings provide a way to study quantum spin systems with irregular geometries beyond the Bethe ansatz approach.

arXiv:2310.11786•Oct 18, 2023•0 citations

Dzyaloshinskii-Moriya interactions effects on the entanglement dynamics of a two qubit xxz spin system in non-Markovian environment

Georges Collince Fouokeng, Martin Tchoffo, Edwine Tendong +1 more

We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.

•May 27, 2014•0 citations

Exact spin helix eigenstates in the anisotropic spin-$s$ Heisenberg model with arbitrary dimensions

Mingchen Zheng, Liang, Chenguang, Shu Chen +1 more

Spin helix states-characterized by their spatially modulated spin textures-are exact eigenstates of the one-dimensional anisotropic spin-$\frac{1}{2}$ Heisenberg model under specific parameter conditions. In this work, we extend this framework by constructing exact spin helix eigenstates for the fully anisotropic XYZ Heisenberg model with arbitrary spatial dimensions and arbitrary spin quantum numbers. Our results demonstrate that some non-trivial exact eigenstates can persist beyond the integrable regime. The XXZ and XY cases are also analyzed to clarify the conditions for the emergence of spin helix eigenstates and their key properties. Our results broaden the class of analytically tractable exact eigenstates in non-integrable systems and deepen understanding of spin modulation states in many-body systems.

arXiv:2505.14994•May 21, 2025•0 citations

Dzyaloshinskii-Moriya interactions effects on the entanglement dynamics of a two qubit xxz spin system in non-Markovian environment

Georges Collince Fouokeng, Martin Tchoffo, Edwine Tendong +1 more

We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.

arXiv:1405.7009•May 27, 2014•2 citations
We systematically investigate possible helix states in the XXZ Heisenberg model with the Dzyaloshinskii-Moriya (DM) interaction. Exact solutions show that a set of precession helix states can be constructed by deliberate superposition of degenerate eigenstates of the Hamiltonian under the resonant condition. When a non-Hermitian balance boundary term is imposed as a quenching action, the quench dynamics shows that a steady helix state emerges from some easily prepared initial states, including saturated and maximally mixed ferromagnetic states, according to the analysis of the perturbation method. The corresponding dynamics for near resonant cases is also investigated numerically, indicating the robustness of the scheme. Our findings highlight the cooperation of non-Hermiticity and the DM interaction in a quantum spin system, suggesting a way for preparing a steady helix state in a non-Hermitian quantum spin system.
Abstract In general, the summation of a set of sub-Hamiltonians cannot share a common eigenstate of each one, only if it is an unentangled product state, such as a spin helix state in quantum spin system. Here we present a method, referred to as the building block method (BBM), for constructing possible spin-1/2 XXZ Heisenberg lattice systems possessing spin helix states. We focus on two types of XXZ dimers as basic elements, with a non-Hermitian parity-time ( P T ) magnetic field and Hermitian Dzyaloshinskii-Moriya interaction (DMI), which share the same degenerate eigenstates. Based on these two building blocks, one can construct a variety of Heisenberg quantum spin systems, which support helix states with zero energy. Furthermore, we show that such systems act as quantum spin graphs since they obey the analogs of Kirchhoff’s laws for sets of spin helix states when the non-Hermitian P T terms cancel each other out. In addition, the dynamic response of the helix states for three types of perturbations is also investigated analytically and numerically. Our findings provide a way to study quantum spin systems on irregular lattices.
Phantom helix states are a special set of degenerate eigenstates of the XXZ Heisenberg model which lie in the energy levels around zero energy and are bidirectionally equal. In this work, we study the helix state in the XXZ Heisenberg model with the Dzyaloshinskii-Moriya interaction (DMI). We show exactly that only the helix states in one direction remain unchanged in the presence of resonant DMI. Based on the Holstein-Primakoff transformation, the quantum spin model is mapped to a boson model, which allows us to understand the underlying mechanism. Furthermore, it also indicates that such phantom states can be separated from the spectrum by the strong DMI to enhance the robustness of the states. We demonstrate the dynamic formation processes of unidirectional phantom helix states by numerical simulations. The results indicate that the DMI, as expected, acts as a filter with high efficiency.
In general, the summation of a set of sub-Hamiltonians cannot share a common eigenstate of each one, only if it is an unentangled product state, such as a phantom helix state in quantum spin system. Here we present a method, referred to as the building block method (BBM), for constructing possible spin-1/2 XXZ Heisenberg lattice systems possessing phantom helix states. We focus on two types of XXZ dimers as basic elements, with a non-Hermitian parity-time (PT ) field and Hermitian Dzyaloshinskii-Moriya interaction (DMI), which share the same degenerate eigenstates. Based on these two building blocks, one can construct a variety of Heisenberg quantum spin systems, which support helix states with zero energy. The underlying mechanism is the existence of a set of degenerate eigenstates. Furthermore, we show that such systems act as quantum spin graphs since they obey the analogs of Kirchhoff's laws for sets of spin helix states when the non-Hermitian PT fields cancel each other out. In addition, the dynamic response of the helix states for three types of perturbations is also investigated analytically and numerically. Our findings provide a way to study quantum spin systems with irregular geometries beyond the Bethe ansatz approach.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
Exact spin helix eigenstates in the anisotropic spin-sss Heisenberg model with arbitrary dimensions
Spin helix states-characterized by their spatially modulated spin textures-are exact eigenstates of the one-dimensional anisotropic spin-12\frac{1}{2}21​ Heisenberg model under specific parameter conditions. In this work, we extend this framework by constructing exact spin helix eigenstates for the fully anisotropic XYZ Heisenberg model with arbitrary spatial dimensions and arbitrary spin quantum numbers. Our results demonstrate that some non-trivial exact eigenstates can persist beyond the integrable regime. The XXZ and XY cases are also analyzed to clarify the conditions for the emergence of spin helix eigenstates and their key properties. Our results broaden the class of analytically tractable exact eigenstates in non-integrable systems and deepen understanding of spin modulation states in many-body systems.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.