SciPost Submission Page
Anisotropic LandauLifshitz Model in Discrete SpaceTime
by Žiga Krajnik, Enej Ilievski, Tomaž Prosen, Vincent Pasquier
 Published as SciPost Phys. 11, 051 (2021)
Submission summary
As Contributors:  Žiga Krajnik 
Arxiv Link:  https://arxiv.org/abs/2104.13863v2 (pdf) 
Date accepted:  20210825 
Date submitted:  20210727 17:57 
Submitted by:  Krajnik, Žiga 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We construct an integrable lattice model of classical interacting spins in discrete spacetime, representing a discretetime analogue of the lattice LandauLifshitz 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 easyaxis and the easyplane regimes in the nonmagnetized 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
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.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2021818 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2104.13863v2, delivered 20210818, doi: 10.21468/SciPost.Report.3410
Strengths
 original construction of an integrable discretization of the anisotropic LandauLifzhitz ferromagnet
 well written manuscript
 numerical results timely with regards to recent works on crossovers 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
LandauLifshitz 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 zerocurvature
condition on an auxiliary lightcone 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 crossovers 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 quasilocal 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.
Anonymous Report 1 on 2021816 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2104.13863v2, delivered 20210816, 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 LandauLifshitz 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 zerocurvature condition on an auxiliary lightcone 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 crossovers 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 quasilocal 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.