Tobias Verhulst, Ben Anthonis, Jan Naudts
We prove three theorems about the use of a counting operator to study the spectrum of model Hamiltonians. We analytically calculate the eigenvalues of the Hubbard ring with four lattice positions and apply our theorems to describe the observed level crossings.
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We show that soft core bosons in two dimensions with a ring exchange term exhibit a tendency for phase separation. This observation suggests that the thermodynamic stability of normal bose liquid phases driven by ring exchange should be carefully examined.
Padé approximants to the many-body Green's function can be built by rearranging terms of its perturbative expansion. The hypothesis that the best use of a finite number of terms of such an expansion is given by the subclass of diagonal Padé approximants is here tested, and largely confirmed, on a solvable model system, namely the Hubbard ring for a variety of site numbers, fillings and interaction strengths.
We have studied a Hubbard ring with alternating site potentials for half filling in presence of a magnetic flux. Using a mean field approach we have calculated the conductivity of such a ring at low and high temperatures. The interplay of correlation, the polarizing field and the chemical modulation in the site potentials tune the conductivity in an interesting fashion. In presence of the modulation in the site energy an appreciable variation in the conductance is observed with the change in flux. Finite size effects are also identified and they are found to be quickly disappearing with increa…
Using a straightforward extension of the analysis of Lieb and Wu, we derive a simple analytic form for the ground state energy of a one-dimensional Hubbard ring in the atomic limit. This result is valid for an \textit{arbitrary} number of lattice sites $L$ and electrons $N \leq L$. Furthermore, our analysis, including an application of the theory of stochastic matrices, provides insight into the degeneracy and spin properties of the ground states in the atomic limit. We give numerical results which illustrate how the atomic limit is approached.
In this paper, we present a study of the electric transport properties of small discrete rings with $3\leq N\leq 6$ sites and $N_{e}<2N$ electrons, which can be seen as a simplified version of real aromatic molecules. In particular, the ring with six sites and six electrons is our prototype of the benzene molecule. It is already known that the Hubbard model itself cannot account for the anisotropy of the diamagnetic susceptibility of the aromatic molecules, which is observed when they are subjected to an external magnetic field perpendicular to their basal plane. Therefore, we propose an exten…
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…
We develop a procedure which systematically generates all conserved operators in the disordered models of interacting fermions. Among these operators, we identify and count the independent and local integrals of motion (LIOM) which represent the hallmark of the many-body localization (MBL). The method is tested first on the prototype disordered chain of interacting spinless fermions. As expected for full MBL, we find for large enough disorder $N_M=2^M-1$ independent and quasi-local LIOM with support on $M$ consecutive sites. On the other hand, the study of the disordered Hubbard chain reveals …
We have implemented the dynamical vertex approximation (D$Γ$A) in its full parquet-based version to include spatial correlations on all length scales and in {\sl all} scattering channels. The algorithm is applied to study the electronic self-energies and the spectral properties of finite-size one-dimensional Hubbard models with periodic boundary conditions (nanoscopic Hubbard rings). From a methodological point of view, our calculations and their comparison to the results obtained within dynamical mean-field theory, plain parquet approximation, and the exact numerical solution, allow us to eva…
We present a method for computing the full probability distribution function of quadratic observables for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo. Especially, in cold atoms experiments with single site resolution, such full counting statistics can be obtained from repeated projective measurements. We demonstrate, that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find exc…
Ring-exchange interactions have been proposed as a possible mechanism for a Bose-liquid phase at zero temperature, a phase that is compressible with no superfluidity. Using the Stochastic Green Function algorithm (SGF), we study the effect of these interactions for bosons on a two-dimensional triangular lattice. We show that the supersolid phase, that is known to exist in the ground state for a wide range of densities, is rapidly destroyed as the ring-exchange interactions are turned on. We establish the ground-state phase diagram of the system, which is characterized by the absence of the exp…
We propose an extended Hubbard model on a 2D Kagome lattice with an additional ring-exchange term. The particles can be either bosons or spinless fermions . At a special filling fraction of 1/6 the model is analyzed in the lowest non-vanishing order of perturbation theory. Such ``undoped'' model is closely related to the Quantum Dimer Model. We show how to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'', a necessary precondition for for a certain type of non-Abelian topological order. Near the ``special'' values, $d = 2 \cos π/(k…
We have done a study with small, imperfect Hubbard rings with exact diagonalization. The results for few-electron rings show, that the imperfection, whether localized or not, nearly always decrease, but can also \emph{increase} the persistent current, depending on the character of the imperfection and the on-site interaction. The calculations are generally in agreement with more specialized studies. In most cases the electron spin plays an important role.
We show exactly that small Hubbard rings exhibit unusual kink-like structures giving anomalous oscillations in persistent current. Singular behavior of persistent current disappears in some cases. In half-filled systems mobility gradually drops to zero with interaction, while it converges to some finite value in non-half-filled cases.
Using the quantum Monte Carlo method, we investigate the spin dynamics of itinerant electrons in the one-dimensional Hubbard system. Based on the model calculation, we have studied the spin-fluctuations in the quarter-filled metallic Hubbard ring, which is aimed at the vanadium ring or chain defined along corner-sharing tetrahedra of LiV$_2$O$_4$, and found the dramatic changes of magnetic responses and spin-fluctuation characteristics with the temperature. Such results can explain the central findings in the recent neutron scattering experiment for LiV$_2$O$_4$.
We investigate the optical conductivity of a Hubbard ring in presence of an impurity by means of exact diagonalization using the Lanczos algorithm. We concentrate thereby on the first excited, open shell state, i.e. on twisted boundary conditions. In the metallic phase a substantial part of the spectral weight lies in the Drude peak, $σ(ω) = Dδ(ω)+ σ_{\rm reg}$. In the non-interacting system, the Drude peak can be visualized in our calculations at $ω= 0$ even for finite chain lengths. Adding the impurity, the main peak is shifted to finite frequencies proportional to the impurity strength. The…
We investigate currents in a quantum ring threaded by a magnetic flux which can be varied in an arbitrary way from an initial value $ϕ_i$ at time $t_i$ to a final value $ϕ_f$ at time $t_f$. Dynamics of electrons in the ring is described by the Hubbard and the extended Hubbard models. We demonstrate that time dependence of the induced current bears information on electron correlations. In the case of the Hubbard model with infinite on--site repulsion we prove that the current for $t>t_f$ is independent of the flux variation before $t_f$. Additionally, this current is fully determined by a solut…
Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
本研究采用复合算符方法探究强关联Mott绝缘体的亚能隙杂质态，发现Mott环态形成依赖能带混合而非拓扑特性，且Mott零点环态在拓扑零点能带与带混合的平庸准平带零点能带中均可形成。
We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U) to intermediate coupling limit ({\it i.e.} away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U)^3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuation…
We study the effect of varying the boundary condition on the spectral function of a finite 1D Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe Ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low energy holon band and its shadow---which span the whole Brillouin zone---and a spinon band present for momenta less than the Fermi momentum. New features related to the…
We test the response to a threading magnetic field of rings of 5-site $C_{4v}$-symmetric repulsive Hubbard clusters connected by weak intercell links; each 5-site unit has the topology of a CuO$_{4}$ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with 8 particles, we take advantage of a novel exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find Superconducting Flux Quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree…
The density-matrix renormalization group method is used to study the ground state of the two-chain zigzag-bond Hubbard model at quarter filling. We show that, with a proper choice of the signs of hopping integrals, the ring exchange mechanism yields ferromagnetic spin correlations between interchain neighboring sites, and produces the attractive interaction between electrons as well as the long-range pair correlations in the spin-triplet channel, thereby leading the system to triplet superconductivity. We argue that this novel mechanism may have possible relevance to observed superconductivity…
We present a full analytical solution of the multiconfigurational strongly-correlated mixed-valence problem corresponding to the $N$-Hubbard ring filled with $N-1$ electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Huckel-annulene problems for rings of variable size. The number and size of these effective Huckel annulen…
We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite…
We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with power-law decay as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization of period h=4e, half of the superconducting flux quantum of h=2e, as recently predicted by mean-field analysis, together with various flux quanta smaller than h=4e. …
In purely repulsive, $C_{4v}$-symmetric Hubbard clusters a correlation effect produces an effective two-body attraction and pairing; the key ingredient is the availability of W=0 pairs, that is, two-body solutions of appropriate symmetry. We study the tunneling of bound pairs in rings of 5-site units connected by weak intercell links; each unit has the topology of a CuO$_{4}$ cluster and a repulsive interaction is included on every site. Further, we test the superconducting nature of the response of this model to a threading magnetic field. We present a detailed numerical study of the two-unit…
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer. Our results are enabled by a variational ansatz that takes full advantage of the maximal set of commu…
The electric-field response of a one-dimensional ring of interacting fermions, where the interactions are described by the extended Hubbard model, is investigated. By using an accurate real-time propagation scheme based on the Chebyshev expansion of the evolution operator, we uncover various non-linear regimes for a range of interaction parameters that allows modeling of metallic and insulating (either charge density wave or spin density wave insulators) rings. The metallic regime appears at the phase boundary between the two insulating phases and provides the opportunity to describe either we…
Exact and mean-field analysis of the role of Hubbard interactions on flux driven circular current in a quantum ring
本文研究了磁通穿过的有序和无序Hubbard量子环中的环形电流，通过精确对角化和Hartree-Fock平均场方法分析了局域和扩展Hubbard相互作用、无序和电子填充对持续电流的影响。
We study the transmission properties of a few-site Hubbard rings with up to second-nearest neighbor coupling embedded to a ring-shaped lead using exact diagonalization. The approach captures all the correlation effects and enables us to include interactions both in the ring and in the ring-shaped lead, and study on an equal footing weak and strong coupling between the ring and the lead as well as asymmetry. In the weakly coupled case, we find fractional periodicity at all electron fillings at sufficiently high Hubbard U, similar to isolated rings. For strongly coupled rings, on the contrary, f…
We prove that the t-J-U model can be deduced from the Hubbard model at a large but finite U by a canonical transformation. We argue that the system may have a metal-insulator transition at a critical on-site Coulomb interaction whose value, however, is smaller than that in previous calculations in which the kinetic energy has a double counting. In a mean field theory and a special choice of the parameters, we show that the metallic state may be equivalent to the gossamer superconducting state proposed by Laughlin recently.
Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many new types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band structure calculations and photoemission experiments on these systems, we include second and third neighbor hopping paramet…
Relaxation to persistent currents in a Hubbard trimer coupled to fermionic baths
研究 Fermi–Hubbard 三聚物耦合费米子冷库时的弛豫，比较多种 Lindblad 主方程，发现全局相干形式可使系统进入携带定向持续自旋电流的最终态。
We summarize briefly the main results obtained within the proposed EDABI method combining Exact Diagonalization of (parametrized) many-particle Hamiltonian with Ab Initio self-adjustment of the single-particle wave function in the correlated state of interacting electrons. The properties of nanoscopic chains and rings are discussed as a function of their interatomic distance R and compared with those obtained by Bethe ansatz for infinite Hubbard chain. The concepts of renormalized orbitals, distribution function in momentum space, and of Hubbard splitting as applied to nanoscopic systems are e…
The operator techniques based on the Jucys-Murphy operators were applied in the procedure of an immediate diagonalization of the one-dimensional Hubbard model. The Young orthogonal basis was given by the irreducible basis of the symmetric group acting on the set of nodes of the magnetic chain. The example of the attractive Hubbard model at the half-filled magnetic rings case was considered where the group $SU(2)\times SU(2)$ acts within the spin and pseudo-spin space. These techniques significantly reduced size of the eigenproblem of the Hubbard Hamiltonian.
We report on an effective Hubbard Hamiltonian approach for the study of electronic correlations in C$_{20}$ isomers, cage, bowl and ring, with quantum Monte Carlo and exact diagonalization methods. The tight-binding hopping parameter, $t$, in the effective Hamiltonian is determined by a fit to density functional theory calculations, and the on-site Coulomb interaction, $U/t$, is determined by calculating the isomers' affinity energies, which are compared to experimental values. For the C$_{20}$ fullerene cage we estimate $t_{\rm cage}\simeq 0.68-1.36$ eV and $(U/t)_{\rm cage} \simeq 7.1-12.2$.…
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