arXiv:1506.06109 · International Journal of Modern Physics B

Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

I. Grusha, M. Z. Menteshashvili, G. I. Japaridze

Published Jan 6, 2016• 6 citations

Abstract

We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model (IHM) with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin S = 1/2 anisotropic XXZ Heisenberg chain with alternating next-nearest-neighbor (NNN) and three-spin couplings in the presence of a uniform and a staggered magnetic field.

DOI: 10.1142/s0217979215502604

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arXiv:1506.06109 · International Journal of Modern Physics B

Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

I. Grusha, M. Z. Menteshashvili, G. I. Japaridze

Published Jan 6, 2016• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0217979215502604

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arXiv:cond-mat/0412033Physical Review BSep 16, 200553 citations

We derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin

S=1/2

Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange.

U=0

, decreases with increasing

U

and tends to zero for $U\ensuremath{\rightarrow}\ensuremath{\infty}$. The amplitude for spin alternation increases with

U

and tends to saturation for $U\ensuremath{\rightarrow}\ensuremath{\infty}$. Charge order dominates below a value

{U}_{c}

, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\uparrow}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\downarrow}}$, which have to be determined self-consistently. For

U<{U}_{c}

both parameters are positive, for

U>{U}_{c}

they have different signs, and for

U={U}_{c}

one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at

{U}_{c}

can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.

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 (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 fluctuations as

t∕U

is increased from the $t∕U\ensuremath{\rightarrow}0$ Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an

S=1∕2

antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of

t∕U

, despite the fact that the moment of the spin Hamiltonian, which depends on transverse spin fluctuations only, in an increasing function of

t∕U

. We also comment on quantitative aspects of the

t∕U

and

1∕S

expansions.