哈伯德模型的相图:团簇隶自旋方法的研究

Phase diagram of the Hubbard model:A cluster slave-spin study

本文回顾了团簇隶自旋方法在哈伯德模型中的研究.基于自旋电荷分离理论,U(1)隶自旋理论方法将电子算符表示成隶自旋(S=1/2)算符和费米子算符的乘积,其中隶自旋算符表示电子的电荷自由度,费米子算符表示电子的自旋自由度.在正方晶格中,基于鞍点近似,证实顺磁态下一阶的金属-绝缘体莫特相变,并通过渐进展开方法得到了反铁磁态下的交错磁化强度和反铁磁能隙在相变点附近的解析关系,系统地研究了该系统交错磁化强度关于相互作用强度和空穴掺杂浓度的依赖关系,并给出了相应的相图.在石墨烯晶格体系中,证实了在半满情形下,在顺磁半金属和反铁磁绝缘体之间不存在过渡的自旋液体态,并发现了顺磁态下的一阶金属-绝缘体莫特相变;研究该系统的压缩率发现范霍夫奇点附近的准粒子密度被相互作用强度极大压制,但是其色散关系的狄拉克锥结构在反铁磁相变发生之前几乎不随相互作用强度变化.同样也给出了石墨烯哈伯德模型在相互作用强度-空穴浓度参数空间的相图.

We review the study of a cluster spin method in the Hubbard model.Based on the spin charge separation theory,the electron operator is decomposed into the product of a fermionic spinon and a slave spin(S=1/2),which represents the physical charge and spin degrees of freedom,respectively.Zeng et al.confirmed the first-order metal-insulator Mott transition in the paramagnetic state in a square lattice based on the saddle point approximation.Moreover,the relationship between the staggered magnetization and the antiferromagnetic gap is established through asymptotic expansion.They systematically investigated the staggered magnetization with doping and coupling strength as parameters.Zeng et al.confirmed the absence of the intermediate spin liquid state in the honeycomb lattice and the first-order metal-insulator Mott transition in the paramagnetic state.The compressibility near van Hove singularity is suppressed most drastically by interaction,while that at low energy(i.e.,near the Dirac points)remains close to the noninteracting one,indicating the robustness of the Dirac cone structure.Similarly,the overall phase diagram of coupling strength(U)-doping plane(δ)is presented.