Crossover from quantum to thermal behaviour in quantum spin liquids.

量子自旋液体(QSL)包含了各种奇异的现象，包括分馏、非平凡的编织激发统计和缺乏长程有序。虽然已经提出了一些候选材料，但由于缺乏局域有序参数，QSL的实验检测仍然具有挑战性。作为寻找“确凿证据”实验特征的一部分，必须详细了解包括中子散射和核磁共振在内的成熟实验技术中QSL的预期特征。因此，我们必须了解自旋液体行为和不可避免的温度存在的相互作用，无论是在理论水平上，还是在确定进一步的潜在实验含义方面。在实验上，拓扑有序相的关键特征是它们的分数激发，例如分数量子霍尔效应的Laughlin准粒子，或自旋冰的磁单极。在有限的温度下，有限密度的这些激发将被热激发。这个项目的目标是研究这些激发对关键系统性质的影响。首先，我们考虑用最近提出的混合态纠缠度量--对数负性来量化的纠缠含量。我们展示了O(1)密度的热激发准粒子如何导致量子关联的消亡，并最终猝死。此外，我们还将研究非零温度下任意子的动力学。特别是，我们希望探索当两种粒子服从非平凡的相互编织统计时，一种粒子的运动如何受到不同物种的热激发准粒子的背景的影响。该项目的长期目标是了解温度对QSL的总体影响，特别是在非零温度下获得实验数据中T=0 QSL状态的特征。

Quantum spin liquids (QSLs) host a variety of exotic phenomena including fractionalisation, nontrivial braiding statistics of excitations, and the absence of long range order. While a number of candidate materials have been proposed, experimental detection of QSLs remains challenging due to the lack of any local order parameter. As part of the search for a `smoking gun' experimental signature, it is crucial to obtain a detailed understanding of the expected features characteristic of QSLs in well-established experimental techniques, including neutron scattering and NMR. We must therefore understand the interplay of spin liquid behaviour and the unavoidable presence of temperature, both at the theoretical level, and in terms of determining further potential experimental implications.Experimentally, the key characteristic of topologically ordered phases is their fractionalised excitations, such as the Laughlin quasiparticles of the fractional quantum Hall effect, or the magnetic monopoles of spin ice. At finite temperature, a finite density of these excitations will be excited thermally. This goal of this project is to study the effect that these excitations have on key system properties. First, we consider the entanglement content, as quantified by the logarithmic negativity, a recently proposed measure of mixed state entanglement. We show how an O(1) density of thermally excited quasiparticles leads to the demise, and eventually sudden death, of quantum correlations. In addition, we will study the dynamics of anyons at nonzero temperature. In particular, we hope to explore how the motion of one species of particle is affected by a background of thermally excited quasiparticles of a different species, when the two species obey nontrivial mutual braiding statistics. The long term goal of the project is to understand the effect of temperature on QSLs in general, with a particular focus on obtaining signatures of the T=0 QSL state in experimental data at nonzero temperatures.