Filled Hubbard Model Research Articles

Quantum Monte Carlo study of superconductivity in rhombohedral trilayer graphene under an electric field

By using the constrained-phase quantum Monte Carlo method, we performed a systematic study of the ground state of the half filled Hubbard model for a trilayer honeycomb lattice. We analyze the effect of the perpendicular electric field on the electronic structure, magnetic property, and pairing correlations. It is found that the antiferromagnetism is suppressed by the perpendicular electric field, especially the long-range parts, and the dominant magnetic fluctuations are still antiferromagnetic. The electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns among various electric fields and interaction strengths. We also found that the $d+id$ pairing correlation is greatly enhanced as the on-site Coulomb interaction is increased. Our intensive numerical results may unveil the nature of the recently observed superconductivity in rhombohedral trilayer graphene under an electric field.

Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.

Frustration effects at finite temperature in the half filled Hubbard model

We investigate the finite temperature properties of the half filled Hubbard model in two dimensions, with onsite interaction (U), in presence of (frustrating) next nearest neighbor hopping (t′) using a semiclassical approximation scheme. We show that introduction of t′ results in a finite temperature pseudogapped (PG) phase that separates the small U Fermi liquid and large U Mott insulator. We map out the PG to normal metal crossover temperature scale (T*) as a function of U and t′. We demonstrate that in the PG phase, the quadratic dependence of resistivity on temperature is violated due to thermally induced spin fluctuations. We conclude with exact diagonalization calculations, that complement our finite temperature results, and indicate the presence of a frustration driven PG state between the Fermi liquid and the Mott insulator at zero temperature as well.

Publisher's Note: Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice [Phys. Rev. B 90 , 035120 (2014)

Publisher's Note: Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice [Phys. Rev. B <b>90</b> , 035120 (2014)

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems.

Strongly correlated electron systems are generally described by tight-binding lattice Hamiltonians with strong local (onsite) interactions, the most popular being the Hubbard model. Although the half-filled Hubbard model can be simulated by Monte Carlo (MC), physically more interesting cases beyond half-filling are plagued by the sign problem. One therefore should resort to other methods. It was demonstrated recently that a systematic truncation of the set of Dyson-Schwinger equations for correlators of the Hubbard, supplemented by a "covariant" calculation of correlators leads to a convergent series of approximants. The covariance preserves all the Ward identities among correlators describing various condensed matter probes. While first-order (classical), second-order (Hartree-Fock or Gaussian), and third-order (Cubic) covariant approximation were worked out, the fourth-order (quartic) seems too complicated to be effectively calculable in fermionic systems. It turns out that the complexity of the quartic calculation in local interaction models,is manageable computationally. The quartic (Bethe-Salpeter-type) approximation is especially important in 1D and 2D models in which the symmetry-broken state does not exists (the Mermin-Wagner theorem), although strong fluctuations dominate the physics at strong coupling. Unlike the lower-order approximations, it respects the Mermin-Wagner theorem. The scheme is tested and exemplified on the single-band 1D and 2D Hubbard model.

Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice

Motivated by ${\mathrm{Mo}}_{3}{\mathrm{S}}_{7}$(dmit)${}_{3}$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second-order perturbation theory, that in the molecular limit, the ground state and the low-energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry-protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangular necklace lattice at two-thirds filling is captured by the ferromagnetic Hubbard-Kondo lattice chain at half-filling. This is consistent with and strengthens previous claims that both the half-filled ferromagnetic Kondo lattice model and the two-thirds filled Hubbard model on the triangular necklace lattice are also in the Haldane phase. A connection between Hund's rules and Nagaoka's theorem is also discussed.

Nature of the Spin Liquid State of the Hubbard Model on a Honeycomb Lattice

Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model. We find three phases-antiferromagnetic, an unusual Z(2) SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z(2) SL state as the likely candidate for the SL phase of the Hubbard model.

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X. They generate relevant terms proportional to X 2 in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U = U c and a spin transition at U = U s > U c . For U < U c singlet superconducting correlations dominate, while for U > U s , the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values U c < U < U s , the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X = 0 . We obtain that the charge transition remains at U c = 0 for X ≠ 0 . Solving the RG equations for the spin sector, we provide an analytical expression for U s ( X ) . The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X < t / 2 where t is the hopping.

Renormalization Group Approach to the One–Dimensional 1/4–Filled Hubbard Model with Alternating on–Site Interactions

The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system, and to the dynamical generation of a gap in the charge excitation spectrum for Ua≠Ub, Ua&gt;0 or Ub&gt;0. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum, and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.

Numerical calculation of correlation functions by boundary condition averaging: test on the one-dimensional Hubbard model

We diagonalize exactly the Hamiltonian of the one-dimensional half filled Hubbard model on small clusters of sites with generalized boundary conditions (BCs), and we calculate various correlation functions. We choose the ratio of the onsite repulsion to the hopping matrix element U t = 1 , i.e. an intermediate regime. By comparing different system sizes, we find that when such correlations are averaged over different BCs, a quick convergence of the correlation functions in their dependence on the cluster size is obtained. In particular, the use of spin-dependent BCs optimizes the results for spin correlation functions.

Ferromagnetism in Hubbard models: Low density route

Thirty years ago the Hubbard model was introduced by Gutzwiller, Hubbard and Kanamori with the main purpose of mimicking the ferromagnetism of transition metals. Soon after, Nagaoka and Thouless pointed out a basic mechanism for ferromagnetism in strongly correlated electron systems by studying the motion of a single hole in a half--filled Hubbard model. This important work was hoped to shed light onto metallic ferromagnetism from the low doping regime. Unfortunately, this low doping route towards ferromagnetism has not been successful as far as rigorous results for finite doping concentrations are concerned. In the work presented here, we start from the opposite limit of low particle concentrations. In this limit we provide the first proof of a fully polarized metallic ground state for a Hubbard model. The proof proceeds by mapping Hubbard ``zigzag'' chains onto a continuum model with an additional degree of freedom and local first Hund's rule coupling. For this model the maximum total spin multiplet is shown to be the unique ground state for infinite Hubbard coupling. Our proof may open a low density route towards the understanding of the ferromagnetism of Hubbard models.

Proof of antiferromagnetism in the half filled Hubbard model in infinite dimensions

We obtain a rigorous condition for the divergence of the staggered susceptibility of the half filled Hubbard model in infinite dimensions by differentiating the exact functional-integral equation for the local Greens function with respect to a staggered magnetic field. In the weak-coupling regime, wemake the reasonable assumption that the high temperature phase without broken symmetry is a Fermi liquid, and proof that the system develops long-range antiferromagnetic order at a finite temperature.

Resonating Hartree-Fock Studies on Electron Correlation and Bond Alternation in the One Dimensional Half Filled Hubbard Model

Effects of the on-site electron-electron Coulomb interaction U on bond alternation in the one dimensional half filled Hubbard model are studied by the resonating Hartree-Fock method. Two kinds of SDW neutral solitons S 0 A and S 0 B exist in a bond alternated lattice which are centered at a long bond and a short bond, respectively. S 0 A enhances but S 0 B suppresses the alternating bond order (ABO) due to bond alternation. Quantum fluctuations in the ground state involve more S 0 A 's than S 0 B 's because the former has lower energy than the latter with increasing bond alternation so that they enhance the ABO in the true ground state and consequently the bond alternation. The spin and singlet pair correlation functions show that electrons tend to make singlet pairs on nearest neighbor short bonds even from small U 's and small bond alternations.

Quantum Fluctuations to Destroy the Antifer-Romagnetic Spin Order in the One Dimensional Half Filled Hubbard Model

Quantum fluctuations in the one dimensional half filled Hubbard model are investigated with the resonating Hartree-Fock method with the orbital optimisation. The optimised Slater determinants include an inhomogenous spin density wave and configurations accommodating some neutral soliton pairs. The short and long range spin orders are destroyed by quantum translational and breathing motions of soliton pairs and gapless Gaussian type fluctuations, respectively. Our calculation suggests that the lowest singlet and triplet excitation branches are the translational modes of breathing neutral soliton pairs dressed with the Gaussian type fluctuations

The half-filled Hubbard model in the pair approximation of the cluster variation method

The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of explicit expressions for the double occupancy and the nearest neighbor correlation functions. The finite temperature analysis is reduced to the numerical solution of only two coupled transcendental equations. The behavior of local magnetic moment, specific heat and correlation functions is given for some typical cases in one and two dimensions. We obtain good qualitative agreement with exact and numerical results in one dimension. The results for finite temperatures show a rapid evolution, with increasing temperature, from a strongly antiferromagnetic behavior to a disordered one; in the high temperature region a maximum (which has been related to a "gradual" metal--insulator transition) is found in the specific heat for very large values of the Coulomb repulsion.

The one‐dimensional 1/4‐filled Hubbard model with alternating interactions

AbstractThe one‐dimensional Hubbard model with different on‐site interaction on the even (Ua) and odd (Ub) sites is considered within the framework of the weak coupling approach. In the case of a 1/4‐filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for Ua ≠ Ub and Ua&gt;0 or Ub&gt;0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next‐nearest neighbour sites is also considered.

Antiferromagnetic spin-waves in the repulsive Hubbard model — a new functional integral formalism

We develop a new functional integral approach to the Hubbard model, which at the saddle point respects rotational invariance and does not a priori assume long-range order (LRO). Using this approach, we study collective spin fluctuations in the repulsive half filled Hubbard model on a square lattice. Our result differs from recent calculations employing the random phase approximation (RPA) in the appearance of an important wave function renormalization factor 0 ≤ R z ≤ 1. The RPA results can be reproduced in a very simple way provided one sets R z = 1 for all U/ t. However, R z becomes very small weak coupling, implying that collective spin-wave modes destroy the LRO for sufficiently small U/ t even at zero temperature. We suggest the possibility that at weak coupling the half filled Hubbard model on a square lattice is an antiferromagnetic insulator without LRO.