# Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains.

@article{deNardis2020SuperdiffusionFE, title={Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains.}, author={Jacopo de Nardis and Sarang Gopalakrishnan and Enej Ilievski and Romain Vasseur}, journal={Physical review letters}, year={2020}, volume={125 7}, pages={ 070601 } }

Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant…

## 25 Citations

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## References

SHOWING 1-10 OF 97 REFERENCES

Kardar-Parisi-Zhang Physics in the Quantum Heisenberg Magnet.

- PhysicsPhysical review letters
- 2019

By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain, it is shown, for the first time, that this is so.

Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport

- PhysicsPhysical Review B
- 2019

We investigate the dynamics of spin in the axially anisotropic Landau-Lifshitz field theory with a magnetic domain-wall initial condition. Employing the analytic scattering technique, we obtain the…

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

- Physics
- 2017

The anomalous nature of spin transport in the XXZ quantum spin chain has been a topic of theoretical interest for some time. Here, the integrability of the underlying dynamics leads to a ballistic…

Far-from-equilibrium spin transport in Heisenberg quantum magnets.

- PhysicsPhysical review letters
- 2014

The far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice is studied and a profound dependence of the decay rate on the wave vector is found.

Nontopological thermal solitons in isotropic ferromagnetic lattices.

- PhysicsPhysical review. B, Condensed matter
- 1995

Analytical approximations of the leading-order asymptotic behavior of the energy in three limiting cases are presented; results for the thermodynamics are very close to spin-wave and/or Bethe-{\it Ansatz} predictions.

Superdiffusion in One-Dimensional Quantum Lattice Models.

- PhysicsPhysical review letters
- 2018

Using the hydrodynamic transport theory, an analytic lower bound is derived on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half-filling, and it is demonstrated that for certain lattice models with isotropic interactions some of the Noether charges exhibit superdiffusive transport at finite temperature and half- filling.

Anomalous Spin Diffusion in One-Dimensional Antiferromagnets.

- PhysicsPhysical review letters
- 2019

Surprisingly, in SU(2)-invariant spin chains in the vicinity of half filling the authors find a crossover from the semiclassical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating superdiffusive spin dynamics.

Soliton Gases and Generalized Hydrodynamics.

- PhysicsPhysical review letters
- 2018

We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which…

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

- PhysicsSciPost Physics
- 2019

We study the dynamics of a spin-\frac{1}{2}12
XXZ chain which is initially prepared in a domain-wall state. We compare
the results of time-dependent Density Matrix Renormalization Group
simulations…

Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains.

- PhysicsPhysical review letters
- 2019

It is shown that a self-consistent treatment of the nature of spin transport in the integrable XXZ spin chain gives superdiffusion, with an effective time-dependent diffusion constant that scales as D(t)∼t^{1/3}.