论文标题
量子时钟模型中BKT过渡的概括的证据
Evidences of the Generalizations of BKT Transition in Quantum Clock Model
论文作者
论文摘要
我们计算了一个尺寸n-state量子时钟模型的基态能量密度$ε（g）$，其中$ g $是耦合，$ n = 3,4,5，...，10,20 $。使用基于Padé近似的方法，我们提取$ε''（g）$或$ε（g）$的单数结构。它们对应于经典2D时钟模型的特定热和自由能。我们发现，对于$ n = 3,4 $，有一个关键点，$ g_c = 1 $。相应2D经典模型的热容量指数为$α= 0.34 \ pm0.01 $ for $ n = 3 $，而$α= -0.01 = -0.01 \ pm 0.01 \ pm 0.01 $ for $ n = 4 $。对于$ n> 4 $，有两个指数奇异性与$ g_ {c1} = 1/g_ {c2} $相关，而$ε（g）$的行为为$ ae^{ - \ frac { - \ frac {| g_c-g_c-g |^σ}}}}+Analytic \ Analytic \ Analytic \ Analytic \ Analytic \ Analytic \ Analytic \ Analytic \ Analytic \ Analytic \ earlation \ earlation \ earlation \ earlation \ term $ g_c $ g_c $。指数$σ$逐渐从$ 0.2 $增长到$ 0.5 $，因为n从5增加到9 $，当$ n> 9 $时，它稳定在0.5。这些相转换应是kosterlitz- thouless Transition的概括，该转换具有$σ= 0.5 $。这些相变的物理图片仍不清楚。
We calculate the ground state energy density $ε(g)$ for the one dimensional N-state quantum clock model up to order 18, where $g$ is the coupling and $N=3,4,5,...,10,20$. Using methods based on Padé approximation, we extract the singular structure of $ε''(g)$ or $ε(g)$. They correspond to the specific heat and free energy of the classical 2D clock model. We find that, for $N=3,4$, there is a single critical point at $g_c=1$.The heat capacity exponent of the corresponding 2D classical model is $α=0.34\pm0.01$ for $N=3$, and $α=-0.01\pm 0.01$ for $N=4$. For $N>4$, There are two exponential singularities related by $g_{c1}=1/g_{c2}$, and $ε(g)$ behaves as $Ae^{-\frac{c}{|g_c-g|^σ}}+analytic\ terms$ near $g_c$. The exponent $σ$ gradually grows from $0.2$ to $0.5$ as N increases from 5 to 9, and it stabilizes at 0.5 when $N>9$. These phase transitions should be generalizations of Kosterlitz-Thouless transition, which has $σ=0.5$. The physical pictures of these phase transitions are still unclear.
