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physica status solidi (b)

Exact Eigenstates of the Hubbard Model Independent of the On‐Site Electron Interaction

Ming-Yong Ye, Xiu‐Min Lin

Published Sep 18, 2017• 5 citations
Publisher

Abstract

Two‐dimensional Hubbard model is important to understand the high temperature superconductivity. We give several methods to construct exact eigenstates of the two‐dimensional Hubbard model that are independent of the on‐site electron interaction. The number of electrons in some eigenstates can be of the order of the lattice sites. It is shown that the existence of eigenstates independent of the electron interactions is a common feature of the extended Hubbard models that have short‐range interactions, and some eigenstates we construct can be used to represent eigenstates of the two‐dimensional Bose–Hubbard model.

DOI
10.1002/pssb.201700321

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Two‐dimensional Hubbard model is important to understand the high temperature superconductivity. We give several methods to construct exact eigenstates of the two‐dimensional Hubbard model that are independent of the on‐site electron interaction. The number of electrons in some eigenstates can be of the order of the lattice sites. It is shown that the existence of eigenstates independent of the electron interactions is a common feature of the extended Hubbard models that have short‐range interactions, and some eigenstates we construct can be used to represent eigenstates of the two‐dimensional Bose–Hubbard model.
Two-dimensional Hubbard model is very important in condensed matter physics. However it has not been resolved though it has been proposed for more than 50 years. We give several methods to construct eigenstates of the model that are independent of the on-site interaction strength UUU.
A two-dimensional model of interacting electrons on a lattice, the Hubbard model, has been studied by means of a numerical simulation technique. Results for the half-filled-band sector are presented for lattices of up to 6\ifmmode\times\else\texttimes\fi{}6 spatial sites, as a function of temperature and electron-electron repulsion UUU. In the ground state, the system is found to exhibit antiferromagnetic long-range order for all values of UUU, although greatly reduced from the mean-field-theory predictions.
We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2{U}^{2}U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.
An exact analytical diagonalization is used to solve the two-dimensional extended Hubbard model (EHM) for a system with finite size. We have considered an EHM including on-site and off-site interactions with interaction energies U and V , respectively, for a square lattice containing 4 × 4 sites at one-eighth filling with periodic boundary conditions, recently treated by Kovacs and Gulacsi (2006 Phil. Mag. 86 2073). Taking into account the symmetric properties of this square lattice and using a translation linear operator, we have constructed a r-space basis only with 85 state-vectors which describe all possible distributions for four electrons in the 4 × 4 square lattice. The diagonalization of the 85 × 85 matrix energy allows us to study the local properties of the above system as a function of the on-site and off-site interactions energies, where we have shown that the off-site interaction encourages the existence of the double occupancies at the first excited state and induces a supplementary conductivity of the system.
Tweaking the Hubbard model Modeling high-temperature superconductivity (HTS) remains extremely challenging. Many researchers believe that the simplest model that captures HTS is the Hubbard model, which accounts for interactions and allows for electrons to hop from one site of a lattice to another. However, even just determining whether the ground state of this model supports superconductivity is tricky. Jiang and Devereaux undertook an extensive computational study based on a method known as density matrix renormalization group. They found that for a particular concentration of empty lattice sites, superconductivity indeed appears as a long-range state, but only if electrons are allowed to hop to sites that are next to their immediate neighbors on the lattice. Science , this issue p. 1424