有限系统中的量子相位交叉
On quantum phase crossovers in finite systems
摘要：
在这项工作中，我们定义了一个正式的概念，量子相位交叉的某些贝特anonymous可解模型。我们采用的方法利用了一个多体可积系统，其中承认一个精确的Bethe anomaly解决方案，到准精确可解的单体薛定谔算子的频谱的精确映射。薛定谔算子势的最小值的分叉决定了交叉耦合。通过考虑特定基态关联函数的行为，这些关联函数可以被识别为有限粒子数多体可积系统中的量子相位交叉。在这种方法中，量子相位交叉的存在不依赖于热力学极限的存在，使得有限系统的应用是可行的。我们研究两个例子的玻色子哈密顿承认二阶交叉。
英文摘要：
In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body Schrödinger operator. Bifurcations of the minima for the potential of the Schrödinger operator determine the crossover couplings. By considering the behaviour of particular ground-state correlation functions, these may be identified as quantum phase crossovers in the many-body integrable system with finite particle number. In this approach the existence of the quantum phase crossover is not dependent on the existence of a thermodynamic limit, rendering applications to finite systems feasible. We study two examples of bosonic Hamiltonians which admit second-order crossovers.
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