热涨落下的低维关联
Low dimensional correlations under thermal fluctuations
摘要：
本文研究了有限温度下，磁场作用下，无带隙相中不同温度$T\neq 0$，动量$q$和频率$ω$下量子自旋$1/2$梯的关联函数.我们使用含时密度矩阵重整化群（T-DMRG）在一些最佳的数值方案计算这些量。我们比较这些相关性的二聚量子自旋链和简单的自旋链，我们用类似的技术计算。我们分析了中间能量模式，并表明，温度的影响导致形成一个基本上色散模式对应于三重态模式的传播在一个不相干的背景下，与色散发生在非常低的温度完全不同。我们比较的低能量部分的频谱与预测的Tomonaga-Luttinger液体场论在有限温度下。我们表明，场论描述了一个非常强大的方式低能量的相关性的频率或温度的自然截止（有效色散）的系统。我们将讨论如何在例如中子散射实验中测试我们的结果。
英文摘要：
We study the correlation functions of quantum spin $1/2$ ladders at finite temperature, under a magnetic field, in the gapless phase at various relevant temperatures $T\neq 0$, momentum $q$ and frequencies $ω$. We compute those quantities using the time dependent density matrix renormalization group (T-DMRG) in some optimal numerical scheme. We compare these correlations with the ones of dimerized quantum spin chains and simple spin chains, that we compute by a similar technique. We analyze the intermediate energy modes and show that the effect of temperature lead to the formation of an essentially dispersive mode corresponding to the propagation of a triplet mode in an incoherent background, with a dispersion quite different from the one occurring at very low temperatures. We compare the low energy part of the spectrum with the predictions of the Tomonaga-Luttinger liquid field theory at finite temperature. We shows that the field theory describes in a remarkably robust way the low energy correlations for frequencies or temperatures up to the natural cutoff (the effective dispersion) of the system. We discuss how our results could be tested in e.g. neutron scattering experiments.
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