Quantum Critical Dynamics of Tensor Networks

张量网络的量子临界动力学

• 批准号: EP/L001578/1
• 负责人: Andrew Green
• 金额: $ 26.5万
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FL001578%2F1
• 关键词: Quantum; Critical; Dynamics; Tensor; Networks

One of the strangest aspects of quantum mechanics is the idea of action at a distance, whereby if two particles are prepared in a certain state relative to one another and then separated to opposite sides of the galaxy, a measurement on one of them will instantaneously tell one about the state of the other. This so worried Einstein that it gave him a deep suspicion about the theory of quantum mechanics. Nevertheless, experiment after experiment has confirmed that that is just how the universe is. If an intuitive understanding of this escapes us, we at least now know how to quantify the amount of this "quantumness" in a measure called entanglement. The situation is even trickier when we think about systems with many particles. In this case we can imagine that every pair of particles might be entangled with one another. An important insight about the real world, however, is that for a variety of reasons usually pairs of particles are not entangled with one another if they are more than a certain distance apart. A certain type of wavefunction can be written down that encodes this idea of a finite range of entanglement mathematically. These states are known as tensor network states.The use of these states is relatively new, but already their impact is profound and far-reaching. They have enabled the behaviour of many-particle quantum systems to be simulated on a computer with unprecedented accuracy. At the same time, insights flowing from the way in which these states behave has enabled us to make some hitherto unsuspected connections between quantum systems - including ultimately a link between the theory of black holes and the quantum mechanics of electrons in certain types of crystals known a quantum critical.In this project we will use tensor network states to try to understand the dynamics of quantum critical systems - systems that in a certain sense are balanced between being classical and quantum mechanical. Our hope is that in doing so, we will find new ways of modelling quantum systems efficiently on computers, new ways of thinking about the quantum world and new ways to harness it to technological ends.

量子力学最奇怪的方面之一是距离作用力的概念，即如果两个粒子准备好相对于另一个粒子处于特定状态，然后分离到银河系的两边，对其中一个粒子的测量将立即告诉其中一个粒子另一个粒子的状态。这让爱因斯坦非常担心，这让他对量子力学理论产生了深深的怀疑。然而，一次又一次的实验已经证实，宇宙就是这样的。如果我们不能直观地理解这一点，我们至少现在知道了如何用一种叫做纠缠的方法来量化这种“量子”的数量。当我们考虑有许多粒子的系统时，情况就更加棘手了。在这种情况下，我们可以想象每一对粒子都可能相互纠缠。然而，关于现实世界的一个重要见解是，由于各种原因，如果两个粒子之间的距离超过一定距离，它们通常不会相互纠缠。可以写下某种类型的波函数，它在数学上对有限范围的纠缠的想法进行了编码。这些状态被称为张量网络状态。这些状态的使用相对较新，但它们的影响已经是深远的。它们使多粒子量子系统的行为能够在计算机上以前所未有的精度进行模拟。与此同时，从这些态的行为方式中获得的见解使我们能够在量子系统之间建立一些迄今未被怀疑的联系--最终包括黑洞理论和某些类型晶体中电子的量子力学之间的联系，即所谓的量子临界。在这个项目中，我们将使用张量网络态来试图理解量子临界系统的动力学--在某种意义上，系统在经典和量子力学之间保持平衡。我们希望，通过这样做，我们将找到在计算机上高效地对量子系统进行建模的新方法，找到思考量子世界的新方法，找到利用量子世界达到技术目的的新方法。

项目成果

Interaction-induced anomalous quantum Hall state on the honeycomb lattice

• DOI: 10.1103/physrevb.89.165123
• 发表时间: 2014-01
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: T. Durić;N. Chancellor;I. Herbut

Transfer matrices and excitations with matrix product states

• DOI: 10.1088/1367-2630/17/5/053002
• 发表时间: 2014-08
• 期刊: New Journal of Physics
• 影响因子: 3.3
• 作者: V. Zauner;D. Draxler;L. Vanderstraeten;M. Degroote;J. Haegeman;M. Rams;V. Stojevic;N. Schuch;F. Verstraete

Time evolution and deterministic optimization of correlator product states

相关器积状态的时间演化和确定性优化

• DOI: 10.1103/physrevb.94.165135
• 发表时间: 2016
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Stojevic V

Quantum Gross-Pitaevskii Equation

量子 Gross-Pitaevskii 方程

• DOI: 10.21468/scipostphys.3.1.006
• 发表时间: 2017
• 期刊: SciPost Physics
• 影响因子: 5.5
• 作者: Haegeman J