奇数格点的XXZ量子自旋链模型的基态能和第一激发能

The ground state energy and first excitation energy of the XXZ quantum spin chain model with an odd sites number

聚焦于周期边界下的XXZ量子自旋链模型,在有能隙的区间内探究其基态能和第一激发能.结果表明:在热力学极限下,模型的基态能和第一激发能与系统的格点数的奇偶性密切相关.当格点数为偶数时,得到与传统研究一致的结果,系统呈现出明确的能隙;当格点数为奇数时,基态能表达式中出现了一个额外的零阶项,同时第一激发能为零,这表明在奇数格点情形下,模型呈现出连续的能谱特征.这为理解XXZ量子自旋链模型的基本性质提供了重要线索,对于量子相变和临界现象的研究具有重要的理论意义和实验指导价值.

This study focuses on the XXZ quantum spin chain model under periodic boundary conditions,investigating its ground state energy and first excitation energy within the energy gap interval.The results indicate that in the thermodynamic limit,the ground state energy and first excitation energy of the model are closely related to the parity of the systemʼs lattice sites.When the number of lattice sites is even,consistent with traditional studies,the system exhibits a well-defined energy gap.However,when the number of lattice sites is odd,we observe an additional zero-order term in the expression for the ground state energy,while the first excitation energy is zero.This suggests that in the case of odd lattice sites,the model exhibits continuous spectrum characteristics.These findings provide important clues for understanding the basic properties of the XXZ quantum spin chain model and are of significant theoretical significance and experimental guidance value for the study of quantum phase transitions and critical phenomena.