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Localization of spin waves in disordered quantum rotors

机译:自旋波在无序量子转子中的定位

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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_(1c) = 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_(1oc) beyond which the quantum tunneling is exponentially suppressed, c ~ e~(-(L/L_(1oc)~(2(θ+1))). At finite temperature T the spin waves propagate by thermal activation over energy barriers that scale as L~θ. Above d_(1c) the system undergoes an order-disorder phase transition with activated dynamics such that the relaxation time grows with the correlation length ξ as τ ~e~(Cξ~θ/T) at finite temperature and as τ ~e~(C'ξ~(2(θ+1)/h~2)) in the vicinity of the quantum critical point.
机译:我们研究存在随机场和随机各向异性的O(N)量子转子系统中的激发动力学。低于下临界尺寸d_(1c)= 4时,系统表现出具有幂律衰减为相关系数的准远程范围。在零温度下,自旋波位于长度尺度L_(1oc)处,超过该长度尺度,量子隧穿被指数抑制,即c〜e〜(-(L / L_(1oc)〜(2(θ+ 1)))。在有限的温度T下,自旋波通过热激活在能垒上扩展为L〜θ。在d_(1c)以上,系统经历了有序-无序相变,并具有激活的动力学,因此弛豫时间随着相关长度ξτ的增长而增长。在有限温度下为〜e〜(Cξ〜θ/ T),在量子临界点附近为τ〜e〜(C'ξ〜(2(θ+ 1)/ h〜2))。

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