SciPost Submission Page
Anisotropic Landau-Lifshitz Model in Discrete Space-Time
by Žiga Krajnik, Enej Ilievski, Tomaž Prosen, Vincent Pasquier
This is not the latest submitted version.
This Submission thread is now published as
|Authors (as registered SciPost users):||Žiga Krajnik|
|Preprint Link:||https://arxiv.org/abs/2104.13863v1 (pdf)|
|Date submitted:||2021-05-05 18:12|
|Submitted by:||Krajnik, Žiga|
|Submitted to:||SciPost Physics|
We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.
Submission & Refereeing History
You are currently on this page
Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2104.13863v1, delivered 2021-07-18, doi: 10.21468/SciPost.Report.3255
The authors construct an integrable space-time discretization of the classical anisotropic Landau-Lifshitz model. The paper is timely, interesting and well-written. I have only a couple of scientific questions/comments:
1) On p6-8 the authors work with “Sklyanin variables” rather than canonical spin variables, which they justify on the grounds that it is “to facilitate the computation”. However, the space-time continuum limits of the models in question are usually discussed in terms of standard spin variables. Also, the explicit formulas for the propagator in Appendix B seem much more complicated than the expressions that arise at the isotropic point in terms of standard spin variables Eqs. D3 and D4. Could the authors clarify why Sklyanin variables are more natural here, and what advantage they offer compared to ordinary spins?
2) On p.18-19 the authors conjecture that (quasi)-local charges protect the easy-plane spin current, as for the spin-1/2 quantum XXZ model. They also note that for their model, the standard local charges arising from the transfer matrix are spin-flip even. However, this is also true in the quantum case. Could the authors elaborate on the obstacles to writing down classical Z-charges? These have been conjectured to arise as a semiclassical limit of quantum Z-charges for some time (e.g. Ref 71).
Finally, I noticed the following typos:
p2: Can be both -> can both be,
p2, p13,p29: Landau-Lifhsitz -> Landau-Lifshitz
Fig. 2 caption: comprising of -> comprising
p6: Algebra A_q becomes non-degenerate-> The algebra A_q…
p8: To enforce it, variable x -> …the variable x
p8: formuale -> formulae, p20: formuae -> formulae
p10: simplifies considerably -> simplify considerably
p11: There is a number -> there are a number
p15: converging -> converges
p15,16,17,20: consistently - > consistent
p20: corresponding the easy-axis -> corresponding to the…