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arXiv 1009.4113cond-mat.str-el
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具有键-电荷相互作用的半填充哈伯德模型的量子phase diagram

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

A. O. Dobry, A. A. Aligia

摘要:

利用量子场论和玻色化,我们确定了一维哈伯德模型的量子相图键电荷相互作用$X$除了通常的库仑排斥$U$在半填充,为小的相互作用值。我们表明,它是必不可少的,以考虑到形式上不相关的条款$X$。它们在重整化群(RG)的流中生成与$X^2$成比例的相关项。这些项使用算子乘积展开来计算。该模型显示了由$U=U_c$处的电荷跃迁和$U=U_s>U_c$处的自旋跃迁分离的三相。对于$U<U_c$,单重态超导关联占主导地位,而对于$U>U_s$,系统处于通常的哈伯德模型中的自旋密度波相。对于中间值$U_c<U<U_s$,该系统是在一个自发二聚键有序波相,这是不存在的普通哈伯德模型与$X=0$。我们得到对于$X \neq 0$,电荷跃迁保持在$U_c=0$.通过求解自旋扇区的RG方程,给出了$U_s(X)$的解析表达式。结果,只有一个可调参数,是在良好的协议与数值计算的$X < t/2$,其中$t$是跳跃。

英文摘要:

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction $X$ in addition to the usual Coulomb repulsion $U$ at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order $X$. They generate relevant terms proportional to $X^2$ in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at $U=U_c$ and a spin transition at $U=U_s>U_c$. For $U<U_c$ singlet superconducting correlations dominate, while for $U>U_s$, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values $U_c<U<U_s$, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with $X=0$. We obtain that the charge transition remains at $U_c=0$ for $X \neq 0$. Solving the RG equations for the spin sector, we provide an analytical expression for $U_s(X)$. The results, with only one adjustable parameter, are in excellent agreement with numerical ones for $X < t/2$ where $t$ is the hopping.

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