相互作用对拓扑相变影响的量子Monte Carlo数值计算
Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
摘要：
我们从理论上研究拓扑相变在四个广义版本的Kane-Mele-哈伯德模型与多达$2\times 18^2$网站。所有模型都没有费米子符号问题，允许在极低温度下进行数值精确的量子蒙特卡罗（QMC）计算。我们直接从零频率单粒子格林函数数值计算了$\mathbb{Z}_2$不变量和自旋陈数$C_σ$，并研究了在不同的在位相互作用强度下紧束缚参数驱动的拓扑相变. $\mathbb{Z}_2$不变量和自旋Chern数是相互补充的，它们表征了拓扑相，并确定了拓扑相变的临界点。虽然数值确定的相边界是几乎相同的不同的系统尺寸，我们发现强系统尺寸依赖的自旋陈数，量子化的值只有在接近热力学极限。对于我们所考虑的哈伯德模型，QMC结果表明，关联效应导致相界相对于非相互作用极限的移动，而没有任何自发对称性破缺。相互作用引起的位移在相互作用中是非微扰的，并且也不能在“简单的”自洽计算中捕获，例如Hartree-Fock。此外，我们的QMC计算表明，从相互作用的量子涨落稳定的系统中的拓扑相的单体条款保持$D_3$对称性的晶格，和不稳定的拓扑相时，单体条款打破$D_3$对称性。
英文摘要：
We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to $2\times 18^2$ sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the $\mathbb{Z}_2$ invariant and spin Chern number $C_σ$ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The $\mathbb{Z}_2$ invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the non-interacting limit, without any spontaneously symmetry breaking. The interaction-induced shift is non-perturbative in the interactions and cannot be captured within a "simple" self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the $D_3$ symmetry of the lattice, and destabilize topological phases when the one-body terms break the $D_3$ symmetry.
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