Modern Physics Letters A

ABSENCE OF P, T VIOLATION IN THE CHIRAL SPIN STATE OF THE HALF-FILLED HUBBARD MODEL

Hideharu Otsu, Toshiro Sato

Published Aug 20, 1990• 0 citations

Abstract

The chiral spin state of the half-filled Hubbard model, taking into account the local SU(2) symmetry was studied. It is pointed out that there is a possibility that P, T invariances are not violated even in the chiral spin state due to the SU(2) symmetry, so that the Chern-Simons term cannot appear.

DOI: 10.1142/s0217732390001815

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Modern Physics Letters A

ABSENCE OF P, T VIOLATION IN THE CHIRAL SPIN STATE OF THE HALF-FILLED HUBBARD MODEL

Hideharu Otsu, Toshiro Sato

Published Aug 20, 1990• 0 citations

Publisher

Abstract

DOI: 10.1142/s0217732390001815

Related papers

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Journal of Physics Condensed MatterFeb 14, 19940 citations

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Charilaos Aneziris, A. P. Balachandran, Ajit Mohan Srivastava

There is a proposal that a 2 + 1 dimensional Lagrangian for an appropriate number of SU(2) doublets of Dirac fields with couplings to an SU(2) gauge field describes the continuum limit of the strongly coupled half-filled Hubbard model. In this paper, we compare the symmetries of these two models and show that the Dirac Lagrangian does have all the symmetries of the latter. In particular, the SU(2) spin rotation symmetry of the latter is shown to be realized as a Pauli-Gürsey symmetry of the Dirac system. The occurrence of the Pauli-Gürsey symmetry in a class of 2 + 1 dimensional Dirac Lagrangians more general than those with SU(2) gauge couplings is pointed out. The Dirac Lagrangian with SU(2) gauge invariance has more symmetries than the half-filled Hubbard system, being in particular Lorentz invariant. Starting with a general ansatz for the continuum Lagrangian and systematically requiring that it fufills the wanted symmetries of the half-filled Hubbard model, a one-parameter family of possible continuum approximations to this model are derived. The Dirac system corresponds to a special value of this parameter. Except for this special case, these approximations are not Lorentz invariant, but they have rotational invariance.There is a proposal that a 2 + 1 dimensional Lagrangian for an appropriate number of SU(2) doublets of Dirac fields with couplings to an SU(2) gauge field describes the continuum limit of the strongly coupled half-filled Hubbard model. In this paper, we compare the symmetries of these two models and show that the Dirac Lagrangian does have all the symmetries of the latter. In particular, the SU(2) spin rotation symmetry of the latter is shown to be realized as a Pauli-Gürsey symmetry of the Dirac system. The occurrence of the Pauli-Gürsey symmetry in a class of 2 + 1 dimensional Dirac Lagrangians more general than those with SU(2) gauge couplings is pointed out. The Dirac Lagrangian with SU(2) gauge invariance has more symmetries than the half-filled Hubbard system, being in particular Lorentz invariant. Starting with a general ansatz for the continuum Lagrangian and systematically requiring that it fufills the wanted symmetries of the half-filled Hubbard model, a one-parameter family of possible continuum approximations to this model are derived. The Dirac system corresponds to a special value of this parameter. Except for this special case, these approximations are not Lorentz invariant, but they have rotational invariance.

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{\mathit{U}}^{2}

. We discuss situations in which, at low temperatures, the chiral term may have a larger effect than the Pauli coupling of electron spins to a magnetic field. We present a model that explicitly demonstrates this. The ground state is a singlet with a gap; hence the spin susceptibility is zero while the chiral susceptibility is finite and paramagnetic.