Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large- z limit
Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large- z limit
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DOI：
10.1103/physrevb.101.035106
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发表时间：
2019-08
影响因子：
3.7
通讯作者：
Sen Zhou;Long Liang;Ziqiang Wang
中科院分区：
文献类型：
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作者：
Sen Zhou;Long Liang;Ziqiang Wang
通过在大晶格配位数z的极限下建立一个动力学的从玻色子平均场理论，并考虑了双占据（doublon）和空（霍隆）位置之间的结合，研究了Hubbard模型中的Mott金属-绝缘体相变.在莫特绝缘的一面，所有的doublons和holons键合在真实的空间中的激子对导致的电荷间隙，理论大大简化到领先的顺序在$1/\sqrt{z}$，并成为精确的无限-z$贝特晶格。在Hubbard $U_c$和相应的双光子密度$n_d^c$，跳跃$\chi_d^c$和双光子-holon配对$\Delta_d^c$的临界值处，得到了连续Mott跃迁的渐近解.我们发现$U_c=U_{\rm BR} [1 -2n_d^c -\sqrt{z}（\chi_d^c +\Delta_d^c））]\simeq0.8U_{\rm BR}$，其中$U_{\rm BR}$是在Kotliar和Ruckenstein的从玻色子公式的静态平均场解中捕获的Gutzwiller近似中Brinkman-Rice跃迁的临界值。因此，Mott跃迁可以被看作是对由doublon-holon束缚引起的Brinkman-Rice跃迁的量子修正。动态平均场理论的结果进行了定量比较，表现出良好的一致性。在没有磁序的情况下，莫特绝缘体是一种具有非零格点间自旋跳跃的U（1）量子自旋液体，它能在大z极限下生存，并提升局域矩的2^N倍简并度。我们证明了在退禁闭相，自旋子通过一个耗散的紧致U（1）规范场耦合到双光子/holon，实现了自旋-电荷分离的无带隙自旋液体Mott绝缘体.
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $z$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $1/\sqrt{z}$, and becomes exact on the infinite-$z$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard $U_c$ and the corresponding doublon density $n_d^c$, hopping $\chi_d^c$ and doublon-holon pairing $\Delta_d^c$ amplitudes. We find $U_c=U_{\rm BR} [1 -2n_d^c -\sqrt{z} (\chi_d^c +\Delta_d^c))] \simeq0.8U_{\rm BR}$, where $U_{\rm BR}$ is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a $U(1)$ quantum spin liquid with nonzero intersite spinon hopping that survives the large-$z$ limit and lifts the $2^N$-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact $U(1)$ gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.