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The European Physical Journal B

Some exact results for one-dimensional two-band SU(2) bosons

Q.-L. Zhang, S.-J. Gu, You‐Quan Li

Published Aug 1, 2004• 4 citations
Publisher
DOI
10.1140/epjb/e2004-00257-y

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We examine zero-temperature one-particle spectral functions for the one-dimensional two-band spinless fermions with different velocities and general forward-scattering interactions. By using the bosonization technique and diagonalizing the model to two Tomonaga-Luttinger liquid Hamiltonians, we obtain general expressions for the spectral functions, which are given in terms of the Appell hypergeometric functions. For the case of identical two-band fermions, corresponding to the SU(2) symmetric spin-1/2 fermions with repulsive interactions, the spectral functions can be expressed in terms of the Gauss hypergeometric function and are shown to recover the double-peak structure suggesting the well-known ``spin-charge'' separation. By tuning the difference in velocities for the two-band fermions, we clarify the crossover in spectral functions from the spin-charge separation to the decoupled fermions. We discuss the relevance of our results to the spin-1/2 Hubbard model under a magnetic field, which can be mapped onto two-band spinless fermions.
In this article, I discuss W.Kohn’s criterion for a metal insulator transition, within the framework of a one band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some intersting miscellaneous results discussed. The Jordan Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the “extra phases” arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e. diamagnetism), and the corresponding “happy fluxes ” for the fermions identified. A curious result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A “spin-statistics ” like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out. 1
In this article, I discuss W. Kohn’s criterion for a metal insulator transition, within the framework of a one-band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some interesting.miscellaneous results discussed. The Jordan-Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the “extra phases” arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e., diamagnetism), and the corresponding “happy fluxes” for the fermions identified. A curious result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A“spin-statistics” like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out.