Localization of spin waves in disordered quantum rotors

Abstract

We study the dynamics of excitations in a system of $O(N)$ quantum rotors in the presence of random fields and random anisotropies. Below the lower critical dimension $d_{\mathrm{lc}}=4$ the system exhibits a quasi-long-range order with a power-law decay of correlations. At zero temperature the spin waves are localized at the length scale $L_{\mathrm{loc}}$ beyond which the quantum tunneling is exponentially suppressed $c\sim e^{-(L/L_{\mathrm{loc}}{)}^{2(\theta +1)}}$. At finite temperature $T$ the spin waves propagate by thermal activation over energy barriers that scales as $L^{\theta }$. Above $d_{\mathrm{lc}}$ the system undergoes an order-disorder phase transition with activated dynamics such that the relaxation time grows with the correlation length $\xi$ as $\tau \sim e^{C{\xi }^{\theta }/T}$ at finite temperature and as $\tau \sim e^{C^{\prime }{\xi }^{2(\theta +1)}/{\hslash }^2}$ in the vicinity of the quantum critical point.

8 pages, 2 figures, revtex4

References in corpus (9)

• Anderson Transitions
• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Random Fields, Topology, and The Imry-Ma Argument
• Statics and dynamics of elastic manifolds in media with long-range correlated disorder
• Long-range correlated random field and random anisotropy O(N) models: A functional renormalization group study
• Localization of disordered bosons and magnets in random fields
• Random field and random anisotropy O(N) spin systems with a free surface
• Non-Gaussian effects and multifractality in the Bragg glass

Cited by in corpus (6)

• Critical behavior of the 2D Ising model with long-range correlated disorder
• Activated dynamic scaling in the random-field Ising model: a nonperturbative functional renormalization group approach
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• An Exactly Solvable Model of Randomly Pinned Charge Density Waves in Two Dimensions
• Interplay of Quantum and Thermal Fluctuations in Two-Dimensional Randomly Pinned Charge Density Waves