论文标题
开放式Haldane-Shastry链：热力学和批判性
The open Haldane-Shastry chain: thermodynamics and criticality
论文作者
论文摘要
我们研究了带有$ bc_n $类型的SU（$ M | n $）的热力学和关键性，具有一般的化学势术语。我们首先根据$ bc_n $ -type图案得出了该模型频谱的完整描述，从中，我们将分区函数的表示形式推导为位于位点依赖性传输矩阵的产物的痕迹。在热力学极限中，该公式根据转移矩阵的连续限极限的perron-frobenius特征值，对每旋转的自由能产生一个简单的表达。评估该特征值我们获得了$ M，N \ le2 $的链的热力学功能的闭合形式表达式。使用此处得出的基于基序的描述，我们详细研究了这些模型的基础状态及其低能激发。通过这种方式，我们确定化学势空间的关键间隔并计算其相应的费米速度。相反，与先前研究的这种类型的模型相反，我们在某些情况下发现了两种具有线性能量 - 质量质量关系的低能量激发。最后，我们通过分析每个自旋的自由能的表达方式的低温行为来确定所有临界阶段的中心电荷。
We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry chain of $BC_N$ type with a general chemical potential term. We first derive a complete description of the spectrum of this model in terms of $BC_N$-type motifs, from which we deduce a representation for the partition function as the trace of a product of site-dependent transfer matrices. In the thermodynamic limit, this formula yields a simple expression for the free energy per spin in terms of the Perron-Frobenius eigenvalue of the continuum limit of the transfer matrix. Evaluating this eigenvalue we obtain closed-form expressions for the thermodynamic functions of the chains with $m,n\le2$. Using the motif-based description of the spectrum derived here, we study in detail the ground state of these models and their low energy excitations. In this way we identify the critical intervals in chemical potential space and compute their corresponding Fermi velocities. By contrast with previously studied models of this type, we find in some cases two types of low energy excitations with linear energy-quasimomentum relation. Finally, we determine the central charge of all the critical phases by analyzing the low-temperature behavior of the expression for the free energy per spin.
