Hubbard模型中的相位弦效应与交互Chern-Simons理论

Phase string effect and mutual Chern-Simons theory of Hubbard model

费米子符号在费米液体理论中至关重要.然而,在Mott绝缘体中,很强的电子Coulomb相互作用抑制了体系的电荷涨落并消除了电子交换带来的费米子符号问题.本文首先回顾二分晶格上Hubbard模型的相位弦理论,从弱关联的费米液体到强关联的反铁磁Mott绝缘体的转变可以由此得到统一理解.在任意Coulomb作用强度U下,我们首先导出Hubbard模型的严格的符号结构.在小U极限下,它回到通常的费米子符号;在大U极限下,它给出了t-J模型的相位弦符号.在半满情形下,我们构造了一种电子分数化的表象,其中,电荷子与自旋子通过演生的交互Chern-Simons规范场相互耦合.由此导出的基态波函数拟设与低能有效理论可以定性刻画Hubbard模型的基态相图.在弱关联区域,费米液体的准粒子由电荷子与自旋子的束缚态构成,其长程相位相干性取决于背景自旋的关联性质.体系的Mott转变可以通过电荷子打开能隙或是通过自旋子玻色凝聚来实现.

The fermion sign plays a dominant role in Fermi liquid theory. However, in Mott insulators, the strong Coulomb interaction suppresses the charge fluctuations and eliminates the fermion signs due to electron permutation. In this article, we first review the phase string theory of the Hubbard model for a bipartite lattice, which unifies the Fermi liquid at weak coupling and the antiferromagnetic Mott insulator at strong coupling. We first derive the exact sign structure of the Hubbard model for an arbitrary Coulomb interaction U. In small U limit, the conventional fermion sign is restored,while at large U limit, it leads to the phase string sign structure of the t-J model. For half filling, we construct an electron fractionalization representation, in which chargons and spinons are coupled to each other via emergent mutual ChernSimons gauge fields. The corresponding ground state ansatz and low energy effective theory capture the ground state phase diagram of the Hubbard model qualitatively. For weak coupling regime, the Fermi liquid quasiparticle is formed by the bound state of a chargon and a spinon, and the long range phase coherence is determined by the background spin correlation. The Mott transition can be realized either by forming the chargon gap or by condensing the background spinons.