arXiv:cond-mat/9411051 · Journal of Physics A Mathematical and General

XXZ model as an effective Hamiltonian for generalized Hubbard models with broken eta -symmetry

Giuseppe Albertini, V. E. Korepin, Andreas Schadschneider

Published May 21, 1995• 18 citations

Abstract

We consider the limit of strong Coulomb attraction for generalized Hubbard models with eta -symmetry. In this limit these models are equivalent to the ferromagnetic spin- 1/2 Heisenberg quantum spin chain. In order to study the behaviour of the superconducting phase in the electronic model under perturbations which break the eta -symmetry we investigate the ground state of the ferromagnetic non-critical XXZ-chain in the sector with fixed magnetization. It turns out to be a large bound state of N magnons. We find that the perturbations considered here lead to the disappearance of the off-diagonal long-range order.

DOI: 10.1088/0305-4470/28/10/004

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arXiv:cond-mat/9411051 · Journal of Physics A Mathematical and General

XXZ model as an effective Hamiltonian for generalized Hubbard models with broken eta -symmetry

Giuseppe Albertini, V. E. Korepin, Andreas Schadschneider

Published May 21, 1995• 18 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/28/10/004

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U

limit, such non-Hermiticity contributes an extra minus sign in the virtual exchange of the particles. As a consequence, the energy of the effective spin model describing the behavior of the ground state and low energy excitations will be reversed. The corresponding ground state experiences a transition from antiferromagnetism to ferromagnetism characterized by the appearance of a non-decaying correlation function. The numerical result indicates that the $\ensuremath{\eta}$-pairing ground state exits in 1D and 2D systems and is insensitive to the disorder. We further propose a protocol to adiabatically generate the $\ensuremath{\eta}$-pairing state. Our results provide a promising approach for the non-Hermitian strongly correlated system.

In this paper we consider the simplified form that a recently introduced general operator description of the Hubbard model on the square lattice with

N_a^2\gg 1

sites, effective transfer integral

t

, and onsite repulsion

U

has in a suitable one- and two-electron subspace. Such an operator description is that consistent with the model exact global symmetry recently extended to

SO(3)\times SO(3)\times U(1)

. There is a large consensus that in the thermodynamic limit

N_a^2\rightarrow\infty

long-range antiferromagnetic order occurs in the spin-density

m=0

ground state of the half-filled Hubbard model on the square lattice. Here we find that the corresponding spontaneous symmetry breaking lowers the symmetry of such a state from

SO(3)\times SO(3)\times U(1)

for

N_a^2\gg 1

large but finite to

[U(2)\times U(1)]/Z_2^2 \equiv [SO(3)\times U(1)\times U(1)]/Z_2

for

N_a^2\rightarrow\infty

. Moreover, we argue that the spin effective lattice being identical to the original lattice is a necessary condition for the occurrence of ground-state long-range antiferromagnetic order in the limit

N_a^2\rightarrow\infty

. Consistently, strong evidence is provided that for very small hole concentration $0

One-band Hubbard model with transverse anisotropy is considered at density of electrons

n=0.4

. It is shown that when the anisotropy is appropriately chosen, the ground state is ferromagnetic with magnetic order perpendicular to the anisotropy. The increasing of the ratio

\frac tU

, where

t

is the hopping parameter and

U

is the Coulomb repulsion, decreases the Curie temperature, and the system arrives at the quantum critical point

(T_C=0)

. The result is obtained introducing Schwinger bosons and slave Fermions representation of the electron operators. Integrating out the spin-singlet Fermi fields an effective Heisenberg model with ferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Owing to the anisotropy, the magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.