We investigate real-space localization in the few-particle regime of the XXZ spin- $1/2$ chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of nonequilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance $\ensuremath{\sigma}(t)$. For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is stronger the more particles are taken into account in the initial condition. We further find that our nonequilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with $\ensuremath{\sigma}(t)\ensuremath{\propto}{t}^{1/4}$.We investigate real-space localization in the few-particle regime of the XXZ spin-$1/2$ chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of nonequilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance $\ensuremath{\sigma}(t)$. For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is stronger the more particles are taken into account in the initial condition. We further find that our nonequilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with $\ensuremath{\sigma}(t)\ensuremath{\propto}{t}^{1/4}$.

arXiv:1607.05664Physical review. B./Physical review. BApr 4, 20176 citations

Subdiffusive spin transport in disordered classical Heisenberg chains

Adam J. McRoberts, Federico Balducci, Roderich Moessner +1 more

We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system deviate substantially from the usual paradigm of diffusive spin hydrodynamics and exhibit a regime of subdiffusive transport with an exponent changing continuously with the parameter of the distribution. We propose a solvable phenomenological model that correctly yields the subdiffusive exponent, thereby linking local fluctuations in the coupling strengths to the long-time, large-distance behavior. It also yields the finite-time corrections to the asymptotic scaling, which can be important in fitting the numerical data. We show how such exponents undergo transitions as the distribution of the coupling gets wider, marking the passage from diffusion to a regime of slow diffusion, and finally to subdiffusion.We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system deviate substantially from the usual paradigm of diffusive spin hydrodynamics and exhibit a regime of subdiffusive transport with an exponent changing continuously with the parameter of the distribution. We propose a solvable phenomenological model that correctly yields the subdiffusive exponent, thereby linking local fluctuations in the coupling strengths to the long-time, large-distance behavior. It also yields the finite-time corrections to the asymptotic scaling, which can be important in fitting the numerical data. We show how such exponents undergo transitions as the distribution of the coupling gets wider, marking the passage from diffusion to a regime of slow diffusion, and finally to subdiffusion.

arXiv:2304.05423Physical review. B./Physical review. BSep 8, 20234 citations

Random fields and quantum dynamics

Takeyuki Hida

Foundations of PhysicsNov 1, 19972 citations

Dynamics of the Classical Heisenberg Chain

Z. Slanič, Harvey Gould, Jan Tobochnik

Computers in PhysicsNov 1, 19913 citations

We investigate real-space localization in the few-particle regime of the XXZ spin-

1/2

chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of nonequilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance $\ensuremath{\sigma}(t)$. For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is stronger the more particles are taken into account in the initial condition. We further find that our nonequilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with $\ensuremath{\sigma}(t)\ensuremath{\propto}{t}^{1/4}$.