Low-temperature phase diagrams of quantum lattice systems .1. Stability for quantum perturbations of classical systems with finitely-many ground states
Low-temperature phase diagrams of quantum lattice systems .1. Stability for quantum perturbations of classical systems with finitely-many ground states
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DOI：
10.1007/bf02179651
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发表时间：
1996-08-01
影响因子：
1.6
通讯作者：
Frohlich, J
中科院分区：
文献类型：
--
作者：
Datta, N;Fernandez, R;Frohlich, J
从具有规则的零温度相图的d≥2维经典晶格系统出发，涉及有限数量的周期基态，我们证明了添加小量子摄动和/或增加温度只会产生其相图的光滑变形。量子扰动可以涉及玻色子或费米子，范围可以是无限的，但随着键的大小呈指数级衰减。对于费米子，相互作用必须由产生和湮灭算符中的偶次单项式给出。我们的方法也可以应用于一些任意系统。我们的分析是基于Pirogov-Sinai理论的扩展到d + 1维的轮廓展开，通过迭代Duhamel公式获得。
Starting from classical lattice systems in d greater than or equal to 2 dimensions with a regular zero-temperature phase diagram, involving a finite number of periodic ground states, we prove that adding a small quantum perturbation and/or increasing the temperature produce only smooth deformations of their phase diagrams. The quantum perturbations can involve bosons or fermions and can be of infinite range but decaying exponentially fast with the size of the bonds. For fermions, the interactions must be given by monomials of even degree in creation and annihilation operators. Our methods can be applied to some anyonic systems as well. Our analysis is based on an extension of Pirogov-Sinai theory to contour expansions in d + 1 dimensions obtained by iteration of the Duhamel formula.