In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential $V$ at the lattice boundary. Such thresholdless surface states, that can be referred to as Tamm-Hubbard BIC states, exist provided that the impurity potential $V$ is attractive (repulsive) and the particle-particle Hubbard interaction $U$ is repulsive (attractive), i.e. for $UV<0$.
The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along with local terms of lower orders. Derived equations for the electron Green's function are solved by iteration for moderate Hubbard repulsions and temperatures. Starting iteration from Green's functions of the Hubbard-I approximation with various distances of poles from the real frequency axis continua of different metallic and insulating solutions are obtaine…
We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U\to \infty and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U\to 0. Power-law singularit…
Attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. In contrast to the `continuum', on a lattice the trap induced density variation can generate a non monotonic profile of the pairing amplitude, and completely modify the spectral signatures of any possible pseudogap phase. Using a tool that fully captures the inhomogeneity and strong thermal fluctuations, we demonstrate how the crucial radio frequency signatures of pairing are `inverted' in a trapped attractive fermion lattice compared to the traditional continuum case. These features would be c…
We study the spectral function of two-leg Hubbard ladders with the time-dependent density matrix renormalization group method (tDMRG). The high-resolution spectrum displays features of spin-charge separation and a scattering continuum of excitations with coherent bands of bound states `leaking' from it. As the inter-leg hopping is increased, the continuum in the bonding channel moves to higher energies and spinon and holon branches merge into a single coherent quasi-particle band. Simultaneously, the spectrum undergoes a crossover from a regime with two minima at incommensurate values of $k_x$…
We systematically investigate the mode dispersion and spectral weight of the elementary excitation spectra in one-dimensional continuum and lattice electron systems by using the RPA, the Luttinger liquid model, and the Hubbard model. Both charge and spin excitations are studied in details and compared among the theoretical models. For the lattice Hubbard model we use both Bethe-ansatz equations and Lanczos-Gagliano method to calculate dispersion and spectral weight separately. We discuss the theoretically calculated elementary excitation spectra in terms of the experimental inelastic light (Ra…
We use Lanczos exact diagonalization to compute the exact exchange-correlation (xc) potential of a Hubbard chain with large binding energy ("the bulk") followed by a chain with zero binding energy ("the vacuum"). Several results of density functional theory in the continuum (sometimes controversial) are verified in the lattice. In particular we show explicitly that the fundamental gap is given by the gap in the Kohn-Sham spectrum plus a contribution due to the jump of the xc-potential when a particle is added. The presence of a staggered potential and a nearest-neighbor interaction V allows to…
Recently, a SU(4) $π$-flux Hubbard model on the honeycomb lattice has been proposed to study the spin-orbit excitations of $α$-ZrCl$_3$ [Phys.~Rev.~Lett. 121.097201~(2017)]. Based on this model with a zigzag edge, we show the edge defects can induce edge flat bands that result in a SU(4) edge ferromagnetism. We develop an effective one-dimensional interaction Hamiltonian to study the corresponding SU(4) spin excitations. Remarkably, SU(4) spin excitations of the edge ferromagnet appear as a continuum covering the entire energy region rather than usual magnons. Through further entanglement entr…
The Kotliar and Ruckenstein slave-boson representation of the Hubbard model allows to obtain an approximation of the charge dynamical response function resulting from the Gaussian fluctuations around the paramagnetic saddle-point in analytical form. Numerical evaluation in the thermodynamical limit yields charge excitation spectra consisting of a continuum, a gapless collective mode with anisotropic zero-sound velocity, and a correlation induced high-frequency mode at $ω\approx U$. In this work we show that this analytical expression obeys the particle-hole symmetry of the model on any biparti…
We study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {\it ansatz} can be achieved both at weak …
We apply a wilsonian renormalization group approach to the continuum limit of the attractive $t-t'$ Hubbard model, taken when the Fermi level is at the Van Hove singularity of the density of states. The model has well-defined scaling properties and the effective couplings display an unbounded flow in the infrared. We determine the leading instabilities by computing the different response functions up to $t' = 0.5 t$. The phase diagram shows a large boundary between superconducting and charge-density-wave phases, that merge in a triple point with a phase separation instability. The latter is re…
The charge dynamical response function of the Hubbard model is investigated on the square lattice in the thermodynamical limit. The obtained charge excitation spectra consist of a continuum, a gapless collective mode with anisotropic zero-sound velocity, and a correlation induced high-frequency mode at $ω\approx U$. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. Its dependence on the on-site Coulomb repulsion $U$ and density is studied in detail. An approximate analytical expr…
We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the $s=1/2$ next-next-nearest neighbor Heisenberg antiferromagnet on the square lattice, with additional 4-spin ring exchange from higher order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters, $t/U$, to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling, $J_r$, which have been varied between 0$J$ and 1…
Motivated by recent work of Lin, Balents, and Fisher (cond-mat/9801285), we compute correlation functions at zero temperature for weakly coupled two-leg Hubbard ladders and (N,N) armchair carbon nanotubes. Lin et al. argued that such systems renormalize towards the SO(8) Gross-Neveu model, an integrable theory. We exploit this integrability to perform the computation at the SO(8) invariant point. Terms breaking this symmetry can be treated systematically in perturbation theory, leading to a model with the same qualitative features. Using said correlators, we determine the optical conductivity,…
In this Rapid Communication we show that low energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially-polarized phase. We then show that for such a FFLO-like state in the low density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free …
We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multi-particle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of t…
The scaling limit of the less than half filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0<n<1) while adjusting the interaction and bandwidth in a such way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find, that similarly to the half filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half filled band and consequently to the chiral…
The energy gap between the ground state and the first excited state of the one-dimensional attractive Bose-Hubbard Hamiltonian is investigated in connection with directed polymers in random media. The excitation gap Δis obtained by exact diagonalization of the Hamiltonian in the two- and three-particle sectors and also by an exact Bethe Ansatz solution in the two-particle sector. The dynamic exponent z is found to be 2. However, in the intermediate range of the size L where UL~O(1), U being the attractive interaction, the effective dynamic exponent shows an anomalous peak reaching high values …
We study XXZ Heisenberg models on frustrated triangular lattices wrapped around a cylinder. In addition to having interesting magnetic phases, these models are equivalent to Bose-Hubbard models that describe the physical problem of adsorption of noble gases on the surface of carbon nanotubes. We find analytical results for the possible magnetization plateau values as a function of the wrapping vectors of the cylinder, which in general introduce extra geometric frustration besides the one due to the underlying triangular lattice. We show that for particular wrapping vectors $(N,0)$, which corre…
I consider a Hubbard-Anderson model which describes localized orbitals in three different atoms hybridized both among themselves and with a continuum of extended states (ES). Using a generalized Schrieffer-Wolf transformation, I derive an effective Kondo model for the interaction between the doublet ground state of the isolated trimer and the ES. For an isoceles trimer with distances a, l, l between the atoms, the Kondo temperature is negligigle for l < a and has a maximum for finite l > a when a is small. The results agree with experiments for a Cr trimer on Au(111). [T. Jamneala et al., Phys…
We propose a framework to study the properties of the Lefschetz thimbles decomposition for lattice fermion models approaching the thermodynamic limit. The proposed set of algorithms includes the Schur complement solver and the exact computation of the derivatives of the fermion determinant. It allows us to solve the gradient flow (GF) equations taking into account the fermion determinant exactly, with high performance. We can find both real and complex saddle points and describe the structure of the Lefschetz thimbles decomposition for large enough lattices to extrapolate the results to the th…
In this paper, we derive lattice models for the narrow moiré bands of the AB-stacked twisted WSe$_2$ homobilayer through continuum model and Wannier orbital construction. Previous work has shown that an approximate SU(4) Hubbard model may be realized by combining spin and layer because inter-layer tunneling is suppressed due to spin $S_z$ conservation. However, Rashba spin-orbit coupling (SOC) was ignored in the previous analysis. Here, we show that a Rashba SOC of reasonable magnitude can induce a finite but very small inter-layer hopping in the final lattice Hubbard model. At total filling $…
Particle-hole continuum in Dirac sea of graphene has a unique window underneath,which in principle leaves a room for bound state formation in the triplet particle hole channel [Phys. Rev. Lett. {\bf 89}, 016402 (2002)]. In this work, we construct appropriate triplet particle-hole operators, and using a repulsive Hubbard type effective interaction, we employ equations of motions to derive approximate eigen-value equation for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range inte…
Hidden antiferromagnetism, persistent valley fluctuations, and $U(6)$ crossovers in triangular-lattice M-point moiré materials via determinantal quantum Monte Carlo
University of Oxford（牛津大学）；Max-Planck-Institut für Physik Komplexer Systeme（马克斯·普朗克复杂系统物理研究所）
Particle-hole continuum (PHC) for massive Dirac fermions in presence of short range interactions, provides an unprecedented opportunity for formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel in undoped system. Both poles are close in energy and are separated from thec continuum of free particle-hole excitations by an energy scale of the order of gap parameter $Δ$. They both disperse linearly with two different velocities reminiscent of spin-charge separation in Luttinger liquids. When the strength of Hubbard interactions is stronger t…
We consider the 2D Hubbard model on the honeycomb lattice, as a model for single layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its non-interacting value and turns out to be isotropic. On the contrary, the interaction produces an asymmetry between the two components o…
We consider a Hubbard-Anderson model which describes localized orbitals in five different sites hybridized both among themselves and with a continuum of extended states. A square planar geometry with an atom at the center is used to represent TBrPP-Co molecules. When the renormalized effective hopping between sites is small compared with a Kondo energy scale determined by the sitecontinuum hybridization, the system can be described as a set of independent Kondo resonances, rather than molecular states. We study the crossover between both regimes and analyze the spectral density of conduction e…
We present theoretical calculations of collective modes of the one-band attractive Hubbard model which is widely used to study the s-wave superfluid phases of atomic Fermi gases of two-hyperfine states loaded in a deep optical lattice. To make our theory applicable for both superconductivity and superfluidity, we assume the more general $t-U-J$ Hamiltonian. Using the functional differentiation we derive Schwinger-Dyson equations for the single-particle Green's functions. The method of Legendre transform is used to give a systematic derivation of the Bethe-Salpeter (BS) equation for the two-par…
We investigate the zero-temperature BCS to Bose-Einstein crossover at the mean-field level, by driving it with the attractive potential and the particle density.We emphasize specifically the role played by the particle density in this crossover.Three different interparticle potentials are considered for the continuum model in three spatial dimensions, while both s- and d-wave solutions are analyzed for the attractive (extended) Hubbard model on a two-dimensional square lattice. For this model the peculiar behavior of the crossover for the d-wave solution is discussed.In particular, in the stro…
