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arXiv:cond-mat/9702009

Mapping spin-charge separation without constraints

Chandler, J. I., Gunn, J. M. F.

Published Jan 31, 1997• 0 citations
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Abstract

The general form of a mapping of the spin and charge degrees of freedom of electrons onto spinless fermions and local `spin'-1/2 operators is derived. The electron Hilbert space is mapped onto a tensor productspin-charge Hilbert space. The single occupancy condition of the t-J model is satisfied exactly without the constraints between the operators required with slave particle methods and the size of the Hilbert space (four states per site) is conserved. The connection and distinction between the physical electron spin and the ``pseudospin'' used in these maps is made explicit. Specifically the pseudospin generates rotations both in spin space and particle-hole space. A geometric description (up to sign) is provided using two component spinors. The form of the mapped t-J Hamiltonian involves the coupling of spin and spinless fermion currents, as one expects.

DOI
10.48550/arxiv.cond-mat/9702009

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The general form of a mapping of the spin and charge degrees of freedom of electrons onto spinless fermions and local `spin'-1/2 operators is derived. The electron Hilbert space is mapped onto a tensor productspin-charge Hilbert space. The single occupancy condition of the t-J model is satisfied exactly without the constraints between the operators required with slave particle methods and the size of the Hilbert space (four states per site) is conserved. The connection and distinction between the physical electron spin and the ``pseudospin'' used in these maps is made explicit. Specifically the pseudospin generates rotations both in spin space and particle-hole space. A geometric description (up to sign) is provided using two component spinors. The form of the mapped t-J Hamiltonian involves the coupling of spin and spinless fermion currents, as one expects.
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We demonstrate an exact local transformation which maps a purely Fermionic many-body system to a system of spinful bosons and spinless fermions, demonstrating a possible path to a non-Fermi-liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a chargelike quasicharge fermion and a spinlike quasispin Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.
We propose a new fermion-spin transformation to implement the charge-spin separation in the large U Hubbard, or the equivalent t-J model. The charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is represented by a hard-core boson. The local constraint for single occupancy is exactly satisfied. Very good agreement with exact solution is obtained for one-dimensional case in the mean field approximation, regarding the total energy, gapless spinon and holon spectra, and the momentum distribution of physical electrons. The same approximation yields good doping dependence of the staggered magnetization in the two-dimensional case.
Using the mapping of the single-occupation space of the t-J model onto the tensor-product space of local spin-1/2 and holon states, the Hubbard operators and their products corresponding to physical quantities are expressed in terms of local spin and holon operators. All relevant operator relations of the t-J model are reproduced by this representation and no projection procedure is needed to remove the redundant degrees of freedom originating from the spin and charge decoupling. It is shown that the time-reversal symmetry requirement makes the essential restriction on the choice of the fictitious spin state associated with the electron-vacancy state in the mapping. The results are critically compared with the treatment of this topic in the paper of Wang and Rice [Phys. Rev. B 49, 4360 (1994)]. \textcopyright{} 1996 The American Physical Society.
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Strongly-correlated fermion systems on a lattice have been a subject of intense focus in the field of condensed-matter physics. These systems are notoriously difficult to solve, even with state-of-the-art numerical methods, especially in regimes of parameters where degrees of freedom compete or cooperate at similar energy and length scales. Here, we introduce a spin-1 slave-particle technique to approximately treat the t-U-V-J fermionic model at arbitrary electron dopings in an economical manner. This formalism respectively maps the original charge and spin degrees of freedom into effective pseudo-spin and pseudo-fermion sectors, which are treated using a self-consistent cluster mean-field method. We study the phase diagram of the model under various conditions and report the appearance of charge and spin stripes within this formalism. These stripes are a consequence of the cluster mean-field treatment of the pseudo-particle sectors and have not been detected in previous slave-particle studies. The results obtained agree qualitatively well with what more reliable numerical methods capture.