Quantum Critical Dynamics of Tensor Networks

量子力学中最奇怪的一个方面是超距作用的概念，即如果两个粒子被准备成相对于彼此的某种状态，然后被分离到星系的两端，对其中一个粒子的测量将立即告诉另一个粒子的状态。这让爱因斯坦非常担心，使他对量子力学产生了深深的怀疑。然而，一个又一个的实验证实了宇宙就是这样的。如果我们无法直观地理解这一点，我们至少现在知道如何用一种叫做纠缠的测量方法来量化这种“量子化”的量。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，通常如果粒子对之间的距离超过一定距离，它们就不会相互纠缠。一种特定类型的波函数可以被写下来，用数学的方式对有限范围的纠缠进行编码。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。他们使得在计算机上以前所未有的精度模拟多粒子量子系统的行为成为可能。与此同时，从这些状态的行为方式中产生的见解使我们能够在量子系统之间建立一些迄今为止未被怀疑的联系-最终包括黑洞理论和某些已知量子临界类型晶体中电子的量子力学之间的联系。在这个项目中，我们将使用张量网络状态来尝试理解量子临界系统的动力学-在某种意义上，在经典和量子力学之间取得平衡的系统。我们的希望是，在这样做的过程中，我们将找到在计算机上有效地模拟量子系统的新方法，找到思考量子世界的新方法，找到利用量子世界实现技术目的的新方法。

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.