Hubbard model, half-filled

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

For the one-dimensional Hubbard model with half-filling electrons, we have iij) = (ny) =, M+ = j — w, and the entanglement is given by... 

To cover the gap between them the Hubbard model Hamiltonian was quite generally accepted. This Hamiltonian apparently has the ability of mimicking the whole spectrum, from the free quasi-particle domain, at U=0, to the strongly correlated one, at U —> oo, where, for half-filled band systems, it renormalizes to the Heisenberg Hamiltonian, via Degenerate Perturbation Theory. Thence, the Heisenberg Hamiltonian was assumed to be acceptable only for rather small t/U values. 

The two-dimensional Hubbard model (1) has been studied extensively. Nesting is excellent in the half-filled band defined by ka a + kb b = -rr and deteriorates gradually as the occupancy moves away from this value. As a consequence [see Eqs. (35) and (36)] the CDW and SDW responses will decrease away from n = 1. There is also a van Hove singularity in the noninteracting electronic density of states at midband. Note that the inclusion of second-neighbor hopping modifies this considerably. 

As mentioned in Section II, LRO in two dimensions can exist only for a real order parameter, that is, for CDW in a half-filled band. This would be the case for BOW in the polymers or the Peierls state, which would be stabilized by transverse hopping or interchain coupling. This is also the case of the CDW state of the n = 1 two-dimensional Hubbard model. All other types of instabilities, such as those treated in the RPA previously in Section V, require three-dimensional coupling to stabilize any LRO. 

This signals the presence of a gap Ap-Tp in the charge degrees of freedom, which has the same origin as the Mott-Hubbard gap in the one-dimensional Hubbard model at half-filling [119]. 

If is wel-known fhaf fhe ground state of a half-filled system of the t (7 Hubbard model is an antiferromagnetic insulator. The antiferromagnetic conditions are given by... 

Indeed this is a theorem for the simple VB model [49] as well as the half-filled Hubbard model [50]. A related type of result applies [51] for Ji-network species decorated with carbene groups. Such results enable one to easily imagine various possibilities for high-spin species, as early noted by Ovchinnikov [52]. 

The interband and vibronic contributions to the infrared properties of the model system have been calculated in the adiabatic, linear-response approximation. Two possible schemes for the occupation of the band states by a number of electrons or holes Np = N/2 (corresponding to half a carrier per molecule) have been considered (i) the case of regular fermion particles with spin, where the lower band only is half filled, (ii) that of spinless fermions, with the lower band completely full. Although no electron correlation term is explicitly included in the Hamiltonian, the latter case represents the situation that is attained, when the on-site correlation of an Hubbard model is U t. 

In this paper, we examine the electron correlation of one-dimensional and quasi-one-dimensional Hubbard models with two sets of approximate iV-representability conditions. While recent RDM calculations have examined linear [20] as well as 4 x 4 and 6x6 Hubbard lattices [2, 57], there has not been an exploration of ROMs on quasi-one-dimensional Hubbard lattices with a comparison to the one-dimensional Hubbard lattices. How does the electron correlation change as we move from a one-dimensional to a quasi-one-dimensional Hubbard model How are these changes in correlation reflected in the required A -repre-sentability conditions on the 2-RDM One- and two-par-ticle correlation functions are used to compare the electronic structure of the half-filled states of the 1 x 10 and 2x10 lattices with periodic boundary conditions. The degree of correlation captured by approximate A -repre-sentability conditions is probed by examining the one-particle occupations around the Fermi surfaces of both lattices and measuring the entanglement with a size-extensive correlation metric, the Frobenius norm squared of the cumulant part of the 2-RDM [23]. 

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