Dynamics of position disordered Ising spins with a soft-core potential

Abstract

We theoretically study magnetization relaxation of Ising spins distributed randomly in a $d$-dimension homogeneous and Gaussian profile under a soft-core two-body interaction potential $\propto 1/[1+(r/R_c{)}^{\alpha }]$ ($\alpha \ge d$), where $r$ is the inter-spin distance and $R_c$ is the soft-core radius. The dynamics starts with all spins polarized in the transverse direction. In the homogeneous case, an analytic expression is derived at the thermodynamic limit, which starts as $\propto \exp (-t^2)$ and follows a stretched-exponential law asymptotically at long time with an exponent $\beta =d/\alpha$. In between an oscillating behaviour is observed with a damping amplitude. For Gaussian samples, the degree of disorder in the system can be controlled by the ratio $l_{\rho }/R_c$ with $l_{\rho }$ the mean inter-spin distance and the magnetization dynamics is investigated numerically. In the limit of $l_{\rho }/R_c\ll 1$, a coherent many-body dynamics is recovered for the total magnetization despite of the position disorder of spins. In the opposite limit of $l_{\rho }/R_c\gg 1$, a similar dynamics as that in the homogeneous case emerges at later time after a initial fast decay of the magnetization. We obtain a stretched exponent of $\beta \approx 0.18$ for the asymptotic evolution with $d=3,\alpha =6$, which is different from that in the homogeneous case ($\beta =0.5$).

7 pages, 5 figures, comments welcome

References in corpus (13)

• A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas
• Homogeneous Atomic Fermi Gases
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas
• Mean-field and stability analysis of two-dimensional flowing soft-core bosons modeling a supersolid
• Realizing distance-selective interactions in a Rydberg-dressed atom array
• Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum
• Fast and efficient preparation of 1D chains and dense cold atomic clouds
• Glassy quantum dynamics of disordered Ising spins
• Emergence of an Ising critical regime in the clustering of 1D soft matter revealed through string variables
• Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

Cited by in corpus (2)

• Many-Body Localization in the Age of Classical Computing
• Rydberg electromagnetically induced transparency and absorption of strontium triplet states in a weak microwave field