It is found that for on-site interaction $U\neq 0$ the local $SU(2)\times SU(2) \times U(1)$ gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral $t=0$ can be lifted to a global $[SU(2)\times SU(2)\times U(1)]/Z_2^2=SO(3)\times SO(3)\times U(1)$ symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with $t>0$. The generator of the new found hidden independent charge global U(1) symmetry is one half the rotated-electron number of singly-occupied sites operator. It is confirmed elsewhere that our results have important physical consequences concerning the further understanding of the unusual properties of the hole-doped cuprates.
Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/$\mathbb{Z}_2^2$ symmetry
Center of Physics of University of Minho and University of Porto（米尼奥大学与波尔图大学物理中心）；CeFEMA, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院 CeFEMA）
On several one-dimensional (1D) and 2D nonbipartite lattices, we study both free and Hubbard interacting lattice fermions when some magnetic fluxes are threaded or gauge fields coupled. First, we focus on finding out the optimal flux which minimizes the energy of fermions at specific fillings. For spin-$1/2$ fermions at half-filling on a ring lattice consisting of odd-numbered sites, the optimal flux turns out to be $\pmπ/2$. We prove this conclusion for Hubbard interacting fermions utilizing a generalized reflection positivity technique, which can lead to further applications on 2D nonbiparti…
In 1989, Lieb proved two theorems about the Hubbard model. One showed that the ground state of the attractive model was a spin singlet state ($S=0$), was unique, and was positive definite. The other showed that the ground state of the repulsive model on a bipartite lattice at half-filling has a total spin given by $|(N_A-N_B)/2|$, corresponding to the difference of the number of lattice sites on the two sublattices divided by two. In the mid to late 1990's, Shen extended these proofs to show that the pseudospin of the attractive model was minimal until the electron number equaled $2N_A$ where …
The ground-state properties of the Hubbard model with attractive local pairing interactions are investigated in the framework of lattice density-functional theory. A remarkable correlation is revealed between the interaction-energy functional $W[\boldsymbolη]$ corresponding to the Bloch-state occupation-number distribution $η_{\boldsymbol{k}σ}$ and the entropy $S[\boldsymbolη]$ of a system of non-interacting fermions having the same $η_{\boldsymbol{k}σ}$. The relation between $W[\boldsymbolη]$ and $S[\boldsymbolη]$ is shown to be approximately linear for a wide range of ground-state representa…
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin d…
We describe here a quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry. The simulator consists of a structured lateral gate confining two dimensional electrons in a quantum well into artificial minima arranged in a hexagonal lattice. The sublattice symmetry breaking is generated by forming an artificial triangular graphene quantum dot (ATGQD) with zigzag edges. The resulting extended Hubbard model generates tunable ratio of tunneling strength to electron-electron interactions and of sublattice symmetry with control over shape. The validity of the simulator is …
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra- and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic st…
We use the $C_{4v}$ symmetry group of the 4-site Hubbard model to construct a ground state variational wave function of two- and four interacting electrons. In the limit $U\rightarrow 0$, ground state energies of the two- and four interacting electrons system is of the order $-4t$. The variational wave function of the four interacting electrons obtained using the $B_1$ irreducible representation is valid for on-site Coulomb repulsion, while the one obtained using the $A_1$ representation is valid for negative values of the Coulomb interaction. The system exhibits antiferromagnetic correlations…
We study the attractive SU($N$) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites $N_A$ $(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU($N$) quantum number. We also show that the ground state exhibits charge density wave order when $|N_A-N_B|$ is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.
Symmetry-Protected Topological Phases in the Triangular Majorana-Hubbard Ladder
Western Washington University（西华盛顿大学）；Stewart Blusson Quantum Matter Institute, University of British Columbia（不列颠哥伦比亚大学斯图尔特·布拉斯量子物质研究所）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the …
The dominating superconducting pairing symmetry of the kagome-lattice Hubbard model is investigated using the determinant quantum Monte Carlo method. The superconducting instability occurs when doping the correlated insulators formed by the Hubbard interaction near the Dirac filling, and the superconducting state exhibits an electron-hole asymmetry. Among the pairing symmetries allowed, we demonstrate that the dominating channel is d-wave in the hole-doped case. This opens the possibility of condensation into an unconventional $d_{x^2-y^2}+id_{xy}$ phase, which is characterized by an integer t…
Symmetry crossover and excitation thresholds at the neutral-ionic transition of the modified Hubbard model
用价键方法计算了均匀间距的N位修正哈伯德模型的基态、电荷密度和激发能。在中性-离子跃迁（NIT）时，基态分别在周期和反周期边界条件下的4 n，4 n +2环中发生对称性交叉.改进的哈伯德模型在成对侧的抗磁性带绝缘体和共价侧的顺磁性莫特绝缘体之间具有连续的NIT。对于有限N的单重态-三重态（ST）、单重态-单重态（SS）和电荷能隙表明，随着U的增加，ST和SS能隙在NIT处闭合，并且电荷能隙仅在那里消失。双N激励将所有奇点约束到对称交叉的约0.1t。NIT被解释为一个本地化的基态（gs）与有限的间隙对侧和扩展的GS与消失的ST和SS的共价侧的间隙。电荷间隙和电荷刚度表明在过渡金属GS，然而，是无条件不稳定的二聚。
We report the results of a Hartree-Fock study applied to interacting electrons moving in two different bipartite lattices: the dice and the Lieb lattices, at half-filling. Both lattices develop ferrimagnetic order in the phase diagram $U$-$λ$, where $U$ is the Hubbard onsite repulsion and $λ$ the Rashba spin-orbit coupling strength. Our main result is the observation of an unexpected multitude of topological phases for both lattices. All these phases are ferrimagnetic, but they differ among themselves in their set of six Chern numbers (six numbers because the unit cells have three atoms). The …
