2D Hubbard Model Research Articles

An efficient method for strongly correlated electrons in one dimension

The one-particle reduced density matrix functional theory in its natural orbital functional (NOF) version is used to study strongly correlated electrons. We show the ability of the Piris NOF 7 (PNOF7) to describe non-dynamic correlation effects in one-dimensional (1D) systems. An extensive study of 1D systems that includes Hydrogen (H) chains and the 1D Hubbard model with periodic boundary conditions is provided. Different filling situations and large sizes with up to 122 electrons are considered. Compared to quasi-exact results, PNOF7 is accurate in different correlation regimes for the 1D Hubbard model even away from the half-filling, and maintains its accuracy when the system size increases. The symmetric and asymmetric dissociations of the linear H chain composed of 50 atoms are described to remark the importance of long-range interactions in presence of strong correlation effects. Our results compare remarkably well with those obtained at the density-matrix renormalization group level of theory.

Fluctuation diagnostics of the finite-temperature quasi-antiferromagnetic regime of the two-dimensional Hubbard model

We study the finite temperature Fermi-liquid to non-Fermi-liquid crossover in the 2D Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behaviour that is itself characterized by a long, but finite, correlation length scale. We perform fluctuation diagnostics to decompose the single-particle self energy into scattering $q$-vector and bosonic frequency contributions. Within this framework we find that the key contributions to the single-particle self energy that give non-Fermi-liquid character, even at weak coupling, are caused by relatively sharp $q=(\pi,\pi)$ spin fluctuations, while the decomposition in the bosonic frequency channel shows a complicated dependence on the relative strengths of zero, positive and negative frequency contributions. Finally, variation in density suggests that the tendency towards non-Fermi-liquid behavior is not substantially different for electron or hole doped systems.

Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model.

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant MonteCarlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.

An analysis of BCS-BEC crossover under three different approaches and evaluation of critical temperature Tlt;subgt;clt;/subgt;

BCS-BEC crossover regimes can be studied using three approaches (i) from 1D and 2D Hubbard model (ii) from two-channel model for system of ultra-cold alkali atoms (iii) via Feshbach resonance method. It has been observed that in 40K, the appearance of the condensate in BCS regime is accompanied by a significant decrease in the width of the non-condensate fraction. The origin of this phenomenon is yet unknown and requires further study. Another important aspect of the BCS-BEC transition is that one studies the nature of the condensate formed when the system is taken across the resonance. It is not known if the condensate is in the intermediate region of resonance then what will happen whether one will take the linear combination of Cooper pairs and tightly bound molecules or some complex state.

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k,\omega)$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

Period 4 stripe in the extended two-dimensional Hubbard model

We study the competition between stripe states with different periods and a uniform $d$-wave superconducting state in the extended 2D Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping $t'$, the preferred period of the stripe decreases. For the values of $t'$ predicted for cuprate high-T$_c$ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at $1/8$ doping. Only at larger doping, $0.18 \lesssim \delta < 0.25$, the period 4 stripe exhibits coexisting $d$-wave superconducting order. The uniform $d$-wave state is only favored for sufficiently large positive $t'$.

Theoretical Study of Unconventional Plasmon Generation by Solving Finite-Size 3D Hubbard Model within Mean Field Approximation

Recent experimental study on Strontium Niobate Oxide system has revealed unconventional plasmons generated due to confinement by oxygen planes. A phenomenological model accompanied the experimental data on that report has suggested that the confined electrons behave as harmonic oscillators. These motivate us to further study the effect of space confinement to the electrons on the formation of unconventional plasmons theoretically. For this purpose, we propose a method of modeling the generation of the unconventional plasmons in a finite system. The dynamics of correlated electrons in this confined system is described using finite-size 3D Hubbard model that is solved within mean field approximation. We study a hypothetical cubic system that consists of 5x5x5 single-orbital atoms. The calculation is done with and without incorporating the on-site Coulomb repulsion. We also consider both restricted and unrestricted mean field treatments to the calculation. Our dielectric function results show that for restricted mean field with U = 0 eV and unrestricted mean field with U ≤ 2 eV, the system is metal and only two and four unconventional plasmons found respectively. While, for U > 2 eV, it becomes insulator and shows more emergence of unconventional plasmons.

Coupled Cluster as an Impurity Solver for Green's Function Embedding Methods.

We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on the non-Hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled one-dimensional (1D) Hubbard model projected onto a single-site impurity problem and a half-filled two-dimensional (2D) Hubbard model projected onto a four-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of Green's function CCSD solver within the Self-Energy Embedding Theory (SEET) with Hartree-Fock (HF) and Green's Function second order (GF2) for the treatment of the environment.

Coupled self-consistent random-phase approximation equations for even and odd particle numbers: Tests with solvable models

Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent RPA (SCRPA) equations already known from the literature. From the equations of the odd particle number case the single particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both, even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and the 1D Hubbard model give very good results.

Tensor networks for complex quantum systems

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory and the understanding of entanglement in quantum many-body systems. Moreover, it has been not-so-long realized that tensor network states play a key role in other scientific disciplines, such as quantum gravity and artificial intelligence. In this context, here we provide an overview of basic concepts and key developments in the field. In particular, we briefly discuss the most important tensor network structures and algorithms, together with a sketch on advances related to global and gauge symmetries, fermions, topological order, classification of phases, entanglement Hamiltonians, AdS/CFT, artificial intelligence, the 2d Hubbard model, 2d quantum antiferromagnets, conformal field theory, quantum chemistry, disordered systems, and many-body localization.

Polarons leave a trace.

Spin and charge interplay leads to stringlike excitations in the 2D Hubbard model

Looking for patterns in an optical lattice

Quantum Simulation One of the simplest models of interacting fermions on a two-dimensional (2D) lattice—the Hubbard model—becomes too tricky to simulate on classical computers as the density of empty lattice sites (holes) increases. Chiu et al. used a quantum microscope to take snapshots of thousands of realizations of the 2D Hubbard model in an optical lattice filled with fermionic lithium atoms at varying hole densities (see the Perspective by Schauss). The authors used pattern recognition algorithms to analyze the images, in which each lattice site was individually resolved. Comparing these patterns to the predictions of several theoretical models, they found the most consistency with the so-called geometric string model. Science , this issue p. [251][1]; see also p. [218][2] [1]: /lookup/doi/10.1126/science.aav3587 [2]: /lookup/doi/10.1126/science.aax6486

Enhanced correlations and superconductivity in weakly interacting partially flat-band systems: A determinantal quantum Monte Carlo study

Motivated by recent experiments realizing correlated phenomena and superconductivity in 2D van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model, and a partially flat band structure containing a non-dispersing region, with identical total non-interacting bandwidth $W$. For both repulsive and attractive weak interactions ($|U| \ll W$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with $U$ an order of magnitude smaller than $W$, we find the presence of a Mott insulating state near half-filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the non-interacting electronic dispersion.

Pairfield fluctuations of a 2D Hubbard model

At temperatures above the superconducting transition temperature, the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here, we study the d-wave pairfield susceptibility of a 2D Hubbard model for a doping which has a pseudogap (PG) and for a doping which does not. In both cases, there will be a region of Kosterlitz–Thouless fluctuations as the transition at TKT is approached. Above this region, we find evidence for pairfield-order parameter-phase fluctuations for dopings with a PG and BCS Cooper pair fluctuations for dopings without a PG.

Exact results for the entanglement in 1D Hubbard models with spatial constraints

We investigate the entanglement in Hubbard models of hardcore bosons in 1D, with an additional hardcore interaction on nearest-neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of particles and system size, whose ratio determines the system filling. At the thermodynamic limit the entropy diverges logarithmically for all fillings, except for half-filling, with the universal prefactor 1/2 due to partial permutational invariance. We show how maximal entanglement can be achieved by controlling the interaction range between the particles and the filling which determines the empty space in the system. Our results show how entangled quantum phases can be created and controlled, by imposing spatial constraints on states formed in many-body systems of strongly interacting particles.

Numerical investigation of spin excitations in a doped spin chain

We study the doping evolution of spin excitations in a 1D Hubbard model and its downfolded spin Hamiltonians, by using exact diagonalization combined with cluster perturbation theory. In all models, we observe hardening (softening) of spin excitations upon electron (hole) doping, which are reminiscent of recent experiments on 2D cuprate materials. We also find that the 3-site and even higher-order terms are crucial for the low-energy effective spin models to reproduce the magnetic spectra of doped Hubbard systems at a quantitative level. To interpret the numerical results, we further employ a strong coupling slave-boson mean-field theory. The mean-field theory provides an intuitive understanding of the overall compact support of dynamic spin structure factors, including the shift of zero-energy modes and change of spin excitation bandwidth with doping. Our results can serve as predictive benchmarks for future inelastic x-ray or neutron scattering experiments on doped 1D antiferromagnetic Mott insulators.

Occupancy Fluctuation Effects on 3D Hubbard Model at Quarter Filling within Dynamical Mean-Field Theory

Research on materials classified into strongly-correlated systems has become a crucial subject due to the strong interactions among the material constituents yielding various exotic physical properties and phenomena. There have been many computational methods developed to address the properties of such systems accurately within the Hubbard model, but most of them require a lot of computational costs to expect good results. In this research, we proposed a new approach within the Dynamical Mean Field Theory (DMFT) framework that requires a simpler and potentially less numerical-cost algorithm. We implemented this algorithm by constructing the local self-energy matrix elements that depend on the occupancy fluctuations. We integrated them over all possible occupancy configurations to obtain the fully interacting Green functions. The resulted Green function matrix was then used to compute the density of states (DOS) and other quantities. We investigated the case of quarter filling. Our computation results showed that pseudogap appeared when the onsite Coulomb repulsion was sufficiently high and tended to diminish as temperature increased. The system preserved its paramagnetic metallic character for all circumstances we studied.

Theoretical Study of Unconventional Plasmons Formation within a Reduced-Size 1D Hubbard Model around a Quarter Filling

Plasmons, which are conventionally known as quanta of electron plasma oscillations in a metal, were discovered unconventionally in an experiment of Strontium Niobate Oxide with oxygen enrichment (SrNbO3,4). Plasmons that revealed in this experiment arose in the visible-ultraviolet range due to a confinement created by additional oxygens forming nanometer-spaced planes. This experimental background motivated us to study the formation of unconventional plasmons in the material by modeling a hypothetical system described by 5-sites linear chain Hubbard model around a quarter filling. The model was then solved by exact diagonalization (ED) method, from which we constructed the corresponding retarded Green function via Lehmann representation. Our interest was to calculate the optical response functions using Kubo formula of the linear response theory. Our results showed that the conventional plasmonic signals got modified by the presence of on-site Coulomb interactions. In addition, we observed that unconventional plasmons, behaving similarly to those found in the experiment, arose when the Coulomb intersite interaction was applied to the calculation.

The victory project v1.0: An efficient parquet equations solver

Victory, i.e.vienna computational tool depository, is a collection of numerical tools for solving the parquet equations for the Hubbard model and similar many body problems. In the current release, we focus on the single-band 2D Hubbard model, based on which generalizations to non-local interactions, multi orbitals and other lattices are straightforward. The parquet formalism is a self-consistent theory at both the single- and two-particle levels, and can thus describe individual fermions as well as their collective behavior on equal footing. This is essential for the understanding of various emergent phases and their transitions in many-body systems, in particular for cases in which a single-particle description fails. Our implementation of victory is in modern Fortran and it fully respects the structure of various vertex functions in both momentum and Matsubara frequency space. We found the latter to be crucial for the convergence of the parquet equations, as well as for the correct determination of various physical observables. In this release, we thoroughly explain the program structure and the controlled approximations to efficiently solve the parquet equations, i.e. the two-level kernel approximation and the high-frequency regulation. Program summaryProgram Title: VictoryProgram Files doi:http://dx.doi.org/10.17632/ym5kscj9sz.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: The parquet equations require the knowledge of the fully irreducible vertex from which all one- and two-particle vertex and Green’s functions are calculated. The underlying two-particle vertex functions are large memory objects that depend on three momenta with periodic boundary conditions and three frequencies with open ones. The coupled diagrams of the parquet equations extend the frequency dependence of the reducible vertex functions to a larger frequency space where, a priori, no information is available.Solution method: The reducible vertex functions are found to possess the simplest structure among all two-particle vertex functions and can be approximated by functions with a reduced number of arguments, i.e. the kernel functions. The open boundary issue of the vertex functions in Matsubara-frequency space is then solved as follows: we solve the parquet equations with the reducible vertex functions whenever it is possible, otherwise we supplement these by the kernel functions.

Effect of Short-Range Correlations on Spectral Properties of Doped Mott Insulators

In the framework of cluster perturbation theory for the 2D Hubbard and Hubbard-Holstein models at low hole doping we have studied the effect of local and short-range correlations in strongly correlated systems on the anomalous features in the electronic spectrum by investigating the fine structure of quasiparticle bands. Different anomalous features of spectrum are obtained as the result of intrinsic properties of strongly correlated electron and polaron bands in the presence of short-range correlations. Particularly, features similar to the electron-like Fermi-pockets of cuprates at hole doping $p\sim0.1$ are obtained without ad hoc introducing a charge density wave order parameter within the Hubbard model in a unified manner with other known peculiarities of the pseudogap phase like Fermi-arcs, pockets, waterfalls, and kink-like features. The Fermi surface is mainly formed by dispersive quasiparticle bands with large spectral weight, formed by coherent low-energy exications. Within the Hubbard-Holstein model at moderate phonon frequencies we show that modest values of local electron-phonon interaction are capable of introducing low-energy kink-like features and affecting the Fermi surface by hybridization of the fermionic quasiparticle bands with the Franck-Condon resonances.