We perform time-resolved exact diagonalization of the Hubbard model with time dependent hoppings on small clusters of up to $12$ sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a photon. We investigate the behavior of the double occupation and spectral function after the pulse for different cluster geometries and on-site potentials. We find impact ionization in all studied geometries except for one-dimensional chains. Adding next-nearest neighbor hopping to the model leads to a significant enhancement of impact ionization, as does disorder and geometric frustration of a triangular lattice.
Half-filled Hubbard Model on a Bethe lattice with next-nearest neighbor hopping
研究了具有最近邻和次最近邻跃迁$t_1$和$t_2$的Bethe晶格上Néel反铁磁性与顺磁金属-绝缘体跃迁（PMIT）之间的相互作用.我们在本文中集中在半填充的情况。对于$t_2/t_1\to 1$，PMIT超过反铁磁相，并显示出类似于V $_2$ O $_3$的情况。在这个参数制度，我们还观察到一个新的磁相。
The extended Hubbard model with an attractive density-density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range $η$-wave superconductivity. Thus, our system provides an example of an interpl…
Spin waves in the zigzag ordered state on a honeycomb lattice are investigated within a Hubbard model with spin-dependent hopping terms. Roles of the emergent Kitaev, Heisenberg, Dzyaloshinskii-Moriya, and symmetric-off-diagonal spin interactions are investigated on the stability of the zigzag order. While the DM interactions are found to destabilize the zigzag order, the secondary spin-dependent hopping terms (associated with structural distortions) are shown to strongly stabilize the zigzag order and account for magnetocrystalline anisotropy, easy axis, and spin wave gap. The calculated spin…
The charge dynamical response function of the $t-t'-U$ Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slightly affects the renormalization of the quasiparticle mass. In contrast a negative $t'/t$ notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density $n \lesssim 0.5$ ($n \gtrsim …
We report a large-scale density-matrix renormalization group study of the lightly doped Hubbard model on 4-leg cylinders at hole doping concentration $δ=12.5\%$. By keeping a large number of states for long system sizes, we are able to reveal a delicate interplay between superconductivity and charge and spin density wave orders tunable via next-nearest neighbor hopping t'. For finite t', the ground state is consistent with that of a Luther-Emery liquid, having `half-filled' charge stripes with power-law superconducting and charge-density-wave correlations of wave-length $λ=1/2δ$, but short-ran…
We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with nearest (t) and next-nearest (t') neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of t' when we vary the electron density $(ρ)$ from half-filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin-polarized and paramagnetic states prevail. We find that the inclusion of a non-frustrating next nearest neighbor hopping stabilizes the fully spin-polarized phase up until |t'/…
We study the ground state phase diagram of the Anderson-Hubbard model with correlated hopping at half filling in one-dimension. The Hamiltonian has a local Coulomb repulsion $U$ and a disorder potential with local energies randomly distributed in the interval $(-W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites have the same amplitude $t$. We identify three different phase…
The interacting Kane-Mele model with a long-range hopping is studied using analytical method. The original Kane-Mele model is defined on a honeycomb lattice. In the work, we introduce a four-lattice-constant range hopping and the on-site Hubbard interaction into the model and keep its lattice structure unchanged. From the single-particle energy spectrum, we obtain the critical strength of the long-range hopping $t_L$ at which the topological transition occurs in the non-interacting limit of the model and our results show that it is independent of the spin-orbit coupling. After introducing the …
We study the Hubbard model on the AB-stacked bilayer honeycomb lattice with a repulsive onsite interaction U in second order perturbation theory and in self-consistent random phase approximation. We determine the changes in the antiferromagnetic magnetic ordering tendencies due to the real and imaginary parts of the selfenergy at the band crossing points. In particular we present an estimate for the threshold value U* below which the magnetic order is endangered by the splitting of the quadratic band touching points into four Dirac points by an interaction-induced interlayer skew hopping. For …
We study photoexcitations in small Hubbard clusters of up to 12 sites, some of which show an increase of the double occupation after the electric field pulse through impact ionization. Here, the time-dependent electromagnetic field is introduced through a Peierls substitution and the time evolution is calculated by exact diagonalization with commutator-free Magnus integrators. As a tool to better analyze the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. This way, we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which show…
Beyond Hubbard: the role of correlated hopping interaction in superconductors and quantum dot devices
Institute of Physics, M. Curie-Skłodowska University（玛丽亚·居里-斯克沃多夫斯卡大学物理研究所）；International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所马格托国际研究中心）
The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics, and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the attractive Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state. In a large negative $U $ limit, the ODLRO ground state corresponds to $η$-spin ferromagnetic states. We also study the system with mixed hopping conf…
We present a microscopic description of molecular magnets by the multi-orbital Hubbard model, which includes the correlated hopping term, i.e. the dependence of electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derived the spin Hamiltonian using the perturbation theory. The magnetic coupling constant between two ions we determined in two different ways: a)from the expression obtained in the perturbation calculus and b)from the analysis of distances between the lowest levels of the energy spectrum obtained by the …
In strongly correlated electron systems the constraint which prohibits the double electron occupation at local sites can be realized by either the infinite Coulomb interaction or the correlated hopping interaction described by the Hubbard operators, but they both render the conventional field theory inapplicable. Relaxing such the constraint leads to a class of correlated hopping models based on the deformed Hubbard operators which smoothly interpolate the locally free and strong coupling limits by a tunable interaction parameter $0\leq λ\leq 1$. Here we propose a coherent state path integral …
