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arXiv 2109.07550cond-mat.str-el
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二维电子液体中的Mott-Hubbard相变

Mott-Hubbard phase transition in 2D electron liquid

Igor N. Karnaukhov, Kateryna Levchuk, Igor N. Dubinski

摘要:

研究了半充满时短程排斥的六角晶格和三角晶格上的费米子液体的行为。在强耦合极限下,出现Mott-Hubbard相态,绝缘体态的主要特征是晶格的双胞。在半填充的绝缘态中,具有动量$k$和$k+π$的费米子通过有效的$λ$ -场耦合,准粒子激发谱中的能隙打开,在单格点Hubbard排斥$U_c$的临界值处发生Mott相变. $U_c=3.904$和$U_c=5.125$分别是六边形和三角形晶格的计算值。根据短程排斥力的大小,计算了光谱中的能隙和基态的能量。所提出的方法是通用的,它是实现了一个任意尺寸和对称性的晶格与短程排斥费米子模型。

英文摘要:

We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+π$ are coupled via the effective $λ$-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~$U_c$. $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.

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