SciPost Submission Page

Anisotropic Landau-Lifshitz Model in Discrete Space-Time

by Žiga Krajnik, Enej Ilievski, Tomaž Prosen, Vincent Pasquier

Submission summary

As Contributors: Žiga Krajnik
Arxiv Link: https://arxiv.org/abs/2104.13863v2 (pdf)
Date accepted: 2021-08-25
Date submitted: 2021-07-27 17:57
Submitted by: Krajnik, Žiga
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Mathematical Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational

Abstract

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.

Published as SciPost Phys. 11, 051 (2021)



Author comments upon resubmission

Revised version.

List of changes

-We have corrected the typos and grammar mistakes pointed out by the referee and several others.
-We have added a few missing DOIs.


Reports on this Submission

Anonymous Report 2 on 2021-8-18 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2104.13863v2, delivered 2021-08-18, doi: 10.21468/SciPost.Report.3410

Strengths

- original construction of an integrable discretization of the anisotropic Landau-Lifzhitz ferromagnet
- well written manuscript
- numerical results timely with regards to recent works on cross-overs from ballistic to superdiffusive behaviors

Weaknesses

- none.

Report

The authors construct an integrable model of classical spins that can
be viewed as a discrete time version of the anisotropic
Landau-Lifshitz ferromagnet. This generalizes recent work by two of
the authors on the construction of an SU(2) symmetric ferromagnet in
Ref. [56].
The authors' construction is based on a discrete zero-curvature
condition on an auxiliary light-cone lattice, the solution of which
defines the elementary "propagator" that maps pairs of physical spins
forward in time. Arguably the key result of the work is the explicit
construction of this propagator by exploiting certain factorization
properties of the Lax operators that solve the discrete zero curvature
conditions. This is a very interesting to to my knowledge original
construction.

The second part of the work focuses on a numerical analysis of
transport properties in the newly constructed anisotropic ferromagnet,
in particular on magnetization transport in thermal equilibrium as
characterized by the spin Drude weight and spin diffusion
constant. This analysis is timely and ties in very nicely with recent
developments in the field such as cross-overs from ballistic
to superdiffusive behaviors in the vicinity of the isotropic (SU(2)
invariant) point. Moreover, the numerical results are suggestive of
the existence of yet unknown quasi-local conservation laws in the
model, and it clearly would be interesting to try to construct them
explicitly.

The manuscript is well written and makes a number of new and interesting
contributions to the field as detailed above. I recommend publication in its
current form.

  • validity: top
  • significance: high
  • originality: top
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2021-8-16 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2104.13863v2, delivered 2021-08-16, doi: 10.21468/SciPost.Report.3408

Report

The authors construct an integrable model of classical spins that can be viewed as a discrete time version of the anisotropic Landau-Lifshitz ferromagnet. This generalizes recent work by two of the authors on the construction of an SU(2) symmetric ferromagnet in Ref. [56].

The authors' construction is based on a discrete zero-curvature condition on an auxiliary light-cone lattice, the solution of which defines the elementary "propagator" that maps pairs of physical spins forward in time. Arguably the key result of the work is the explicit construction of this propagator by exploiting certain factorization properties of the Lax operators that solve the discrete zero curvature conditions. This is a very interesting and to my knowledge original construction.

The second part of the work focuses on a numerical analysis of transport properties in the newly constructed anisotropic ferromagnet, in particular on magnetization transport in thermal equilibrium as
characterized by the spin Drude weight and spin diffusion constant. This analysis is timely and ties in very nicely with recent developments in the field such as cross-overs from ballistic to superdiffusive behaviors in the vicinity of the isotropic (SU(2) invariant) point. Moreover, the numerical results are suggestive of the existence of yet unknown quasi-local conservation laws in the model, and it clearly would be interesting to try to construct them explicitly.

The manuscript is well written and makes a number of new and interesting contributions to the field as detailed above. I recommend publication in its current form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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