Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore.
J Chem Phys. 2013 Oct 28;139(16):164103. doi: 10.1063/1.4825205.
We have carried out analytical and numerical studies of the spin-boson model in the sub-ohmic regime with the influence of both the diagonal and the off-diagonal coupling accounted for, via the Davydov D1 variational ansatz. While a second-order phase transition is known to be exhibited by this model in the presence of diagonal coupling only, we demonstrate the emergence of a discontinuous first order phase transition upon incorporation of the off-diagonal coupling. A plot of the ground state energy versus magnetization highlights the discontinuous nature of the transition between the isotropic (zero magnetization) state and nematic (finite magnetization) phases. We have also calculated the entanglement entropy and a discontinuity found at a critical coupling strength further supports the discontinuous crossover in the spin-boson model in the presence of off-diagonal coupling. It is further revealed via a canonical transformation approach that for the special case of identical exponents for the spectral densities of the diagonal and the off-diagonal coupling, there exists a continuous crossover from a single localized phase to doubly degenerate localized phase with differing magnetizations.
我们通过 Davydov D1 变分近似，对具有对角和非对角耦合影响的亚欧姆区域的自旋-玻色子模型进行了分析和数值研究。虽然该模型在仅存在对角耦合时已知会表现出二阶相变，但我们证明了在包含非对角耦合时会出现不连续的一阶相变。基态能量与磁化强度的关系图突出显示了各向同性（零磁化强度）状态和向列（有限磁化强度）相之间的转变的不连续性。我们还计算了纠缠熵，在临界耦合强度处发现的不连续性进一步支持了存在非对角耦合时自旋-玻色子模型的不连续交叉。通过正则变换方法进一步揭示，对于对角和非对角耦合的谱密度具有相同指数的特殊情况，从单个局域相到具有不同磁化强度的双简并局域相存在连续交叉。
