论文标题
有限组件动力学量子相变
Finite-component dynamical quantum phase transitions
论文作者
论文摘要
最近已经在量子多体系统的时域提出了相变，该现象称为动态量子相变（DQPTS），其现象学通常分为两种类型。一个是根据长期平均顺序参数指的不同阶段，而另一个则集中在Loschmidt Echo的速率函数中出现的非分析行为。在这里，我们证明可以在几乎没有自由度的系统中找到此类DQPT，即可以在不诉诸传统热力学极限的情况下进行。我们通过在量子狂犬模型中显示两种类型的DQPT的存在来说明这一点 - 涉及自旋 - $ \ frac {1} {2} {2} $的系统和Bosonic模式。动力学临界性出现在旋转频率相对于骨频率的极限之比的极限。我们确定其动力学相图并研究长期平均顺序参数，其半经典近似在过渡点产生了跳跃。我们发现速率函数变为非分析的关键时期，显示其相关的临界指数以及有限频率比引入的校正。我们的结果为研究DQPT的研究打开了大门，而无需扩大组件的数量，从而可以在可控制的系统中进行调查。
Phase transitions have recently been formulated in the time domain of quantum many-body systems, a phenomenon dubbed dynamical quantum phase transitions (DQPTs), whose phenomenology is often divided in two types. One refers to distinct phases according to long-time averaged order parameters, while the other is focused on the non-analytical behavior emerging in the rate function of the Loschmidt echo. Here we show that such DQPTs can be found in systems with few degrees of freedom, i.e. they can take place without resorting to the traditional thermodynamic limit. We illustrate this by showing the existence of the two types of DQPTs in a quantum Rabi model -- a system involving a spin-$\frac{1}{2}$ and a bosonic mode. The dynamical criticality appears in the limit of an infinitely large ratio of the spin frequency with respect to the bosonic one. We determine its dynamical phase diagram and study the long-time averaged order parameters, whose semiclassical approximation yields a jump at the transition point. We find the critical times at which the rate function becomes non-analytical, showing its associated critical exponent as well as the corrections introduced by a finite frequency ratio. Our results open the door for the study of DQPTs without the need to scale up the number of components, thus allowing for their investigation in well controllable systems.
