论文标题
具有自由费用和偏僻的量子链的整合量子自旋链
Integrable quantum spin chains with free fermionic and parafermionic spectrum
论文作者
论文摘要
我们介绍了一项对\ cite {ap2020}最近引入的多动相互作用的大型精确整合量子链的一般研究。确切的集成性来自定义量子链的能量密度运算符的代数性能。汉密尔顿人的特征是参数$ p = 1,2，\点$与多刺相互作用中的相互作用旋转数量有关。在一般情况下，量子旋转是无限的尺寸。在特殊情况下，以参数$ n = 2,3，\ ldots $为特征，量子链描述了$ z（n）$量子旋转链的动力学。最简单的情况$ p = 1 $对应于免费的费米子量子ising链（$ n = 2 $）或$ z（n）$ free Parafermionic量子链。量子链的特征力是根据特殊多项式的根源给出的，对于$ p $的一般值，量子链的特征是免费的费米子（$ n = 2 $）或免费的parafermionic（$ n> 2 $）特征。当所有耦合常数均等时，模型具有特殊的临界点。在这一点上，基本能量是在大量限制中精确计算的，我们的分析和数值分析表明，模型属于具有动态临界指数的临界行为的通用类别$ z =（p+1）/n $以及特定的热指数$α= \ axmax = \ max \ {0,1-（p+1）/n \} $。
We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,\dots$ related to the number of interacting spins in the multispin interaction. In the general case the quantum spins are of infinite dimension. In special cases, characterized by the parameter $N=2,3,\ldots$, the quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The simplest case $p=1$ corresponds to the free fermionic quantum Ising chain ($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of $p$ the quantum chains are characterized by a free fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent $z = (p+1)/N$ and specific-heat exponent $α= \max\{0,1-(p+1)/N\}$.
