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Bridging Quantum and Classical Descriptions of Spin Dynamics in a Dzyaloshinsky-Moriya Trimer

Robert Wieser, Raúl Sánchez Galán

Abstract

The spin dynamics of a trimer with Dzyaloshinsky-Moriya (DM) interaction are investigated within a unified Hamiltonian framework that connects quantum-mechanical and semiclassical descriptions. The interpolation between the two regimes is realised by solving the modified Gisin-Schrödinger equation, in which the relative weight of a quantum coherence and local mean-field contributions is continuously tuned. The resulting dynamical behaviour is analysed and summarised in a ground state diagram that illustrates how the character of the spin motion evolves from fully quantum to semiclassical as the DM interaction is treated at different levels of approximation. In the last part of the publication, the chiral spin dynamics proposed by Da-Wei Wang et al. is examined theoretically, taking into account its behaviour at the boundary between quantum and classical physics.

Bridging Quantum and Classical Descriptions of Spin Dynamics in a Dzyaloshinsky-Moriya Trimer

Abstract

The spin dynamics of a trimer with Dzyaloshinsky-Moriya (DM) interaction are investigated within a unified Hamiltonian framework that connects quantum-mechanical and semiclassical descriptions. The interpolation between the two regimes is realised by solving the modified Gisin-Schrödinger equation, in which the relative weight of a quantum coherence and local mean-field contributions is continuously tuned. The resulting dynamical behaviour is analysed and summarised in a ground state diagram that illustrates how the character of the spin motion evolves from fully quantum to semiclassical as the DM interaction is treated at different levels of approximation. In the last part of the publication, the chiral spin dynamics proposed by Da-Wei Wang et al. is examined theoretically, taking into account its behaviour at the boundary between quantum and classical physics.
Paper Structure (8 sections, 32 equations, 7 figures)

This paper contains 8 sections, 32 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Theoretical Model
  3. Description of the trimer using a quantum to classical spin dynamics bridging
  4. Spin dynamics caused by the chirality
  5. Summary
  6. Relaxation dynamics towards eigenstates of $\hat{\mathrm{H}}$
  7. Connection between the modified Gisin-Schrödinger and the LLG equation
  8. von Neumann Entropy

Figures (7)

  • Figure 1: Ground state diagram: magnetic field $B$ over the local mean-field contribution to the Dzyaloshinsky-Moriya interaction $D_{\mathrm{LMF}}$. The dotted lines represent the calculated boundaries of the different quantum states. Details regarding the quantum states and crossover can be found in the text.
  • Figure 2: Magnetization, principal angle, chirality, and von Neumann entropy (as a measure of entanglement) as functions of the classicality parameter $D_{\mathrm{LMF}}$ in the absence of an external magnetic field, $B = 0$.
  • Figure 3: Magnetization, principal angle, chirality, and von Neumann entropy (as a measure of entanglement) as functions of the classicality parameter $D_{\mathrm{LMF}}$, for a constant magnetic field $B = 0.4$.
  • Figure 4: Magnetization, principal angle, chirality, and von Neumann entropy (as a measure of entanglement) as functions of the external magnetic field $B$, at constant classicality $D_{\mathrm{LMF}} = 0.7$.
  • Figure 5: Magnetization, principal angle, chirality, and von Neumann entropy (as a measure of entanglement) as functions of the external magnetic field $B$, at constant classicality $D_{\mathrm{LMF}} = 0.1$.
  • ...and 2 more figures