Zhirov O V, Casati G, Shepelyansky D L
Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 2):056209. doi: 10.1103/PhysRevE.67.056209. Epub 2003 May 19.
We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime where the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By extensive quantum Monte Carlo simulations, we show that for the effective Planck constant Planck smaller than the critical value Planck(c) the quantum chain is in the pinned instanton glass phase. In this phase, the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons that have an exponentially small excitation energy. At Planck = Planck(c) the quantum phase transition takes place and for Planck > Planck(c) the pinned instanton glass is transformed into the sliding phonon gas with gapless phonon excitations. This transition is accompanied by the divergence of the spatial correlation length and appearance of sliding modes at Planck > Planck(c).
我们通过解析和数值方法研究了一维量子弗伦克尔 - 康托洛娃链，该经典模型处于以能隙声子激发和魔鬼阶梯为特征的钉扎相。通过广泛的量子蒙特卡罗模拟，我们表明，对于有效普朗克常数普朗克小于临界值普朗克（c）的情况，量子链处于钉扎瞬子玻璃相。在这个相中，元激发有两个分支：声子，与零能量之间存在有限能隙；以及具有指数级小激发能量的瞬子。在普朗克 = 普朗克（c）时发生量子相变，并且对于普朗克 > 普朗克（c），钉扎瞬子玻璃转变为具有无隙声子激发的滑动声子气体。这种转变伴随着空间关联长度的发散以及在普朗克 > 普朗克（c）时滑动模式的出现。
