Sub-Ohmic spin-boson model with off-diagonal coupling: ground state properties.
Sub-Ohmic spin-boson model with off-diagonal coupling: ground state properties.
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DOI：
10.1063/1.4825205
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发表时间：
2013-10
期刊：
影响因子：
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通讯作者：
Z. Lü;Liwei Duan;Xin Li;P. Shenai;Yang Zhao
中科院分区：
文献类型：
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作者：
Z. Lü;Liwei Duan;Xin Li;P. Shenai;Yang Zhao
我们通过Davydov D1变分分析对亚欧姆区域的自旋玻色子模型进行了分析和数值研究，考虑了对角线和非对角线耦合的影响。虽然已知该模型仅在存在对角耦合的情况下表现出二阶相变，但我们证明了在纳入非对角耦合后出现不连续的一阶相变。基态能量与磁化的关系图突出了各向同性（零磁化）和向列相（有限磁化）相变之间的不连续性质。我们还计算了纠缠熵，在临界耦合强度处发现的不连续进一步支持了自旋玻色子模型中存在非对角耦合时的不连续交叉。通过正则变换方法进一步揭示了在对角线和非对角线耦合的谱密度指数相同的特殊情况下，存在从单一局域相到不同磁化强度的双简并局域相的连续交叉。
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.