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.
Discussed are the generic predictions of theories based upon the spinon-holon picture. In such theories there is a separation of the charge degrees of freedom associated with the holons and the spin degrees of freedom associated with the spinons. The nature of the spinon ground state, near to halt filling (one physical electron per site) is of key importance. There are two general classes of spinon ground states. One class consists of ground states which cause there to exist a fictitious magnetic flux, either time independent or fluctuating. Within the second class there exists a BCS pair amplitude. While, at half filling, these two types of pairing are equivalent, by virtue of an SU(2) symmetry, for a finite doping, the predictions for the momentum distribution are quite different. These generic issues are illustrated by simple model calculations.
An exact expression for the Hamiltonian H of the t-J model in terms of local spin (
Si) and fermionic holon (
ei) operators is derived which requires no constraint between these operators. The result for the Hamiltonian H is H=-t t
sumijei${\mathit{e}}_{\mathit{j}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$(1/2+2
Si\ensuremath{\cdot}
Sj)+(J/2)t
smij(1-${\mathit{e}}_{\mathit{i}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$
ei)(
Si\ensuremath{\cdot}
Sj-1/4)(1-${\mathit{e}}_{\mathit{j}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$e The number of electrons at site i is given by
ni=1-${\mathit{e}}_{\mathit{i}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$
ei, and the true spin operator S${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{i}}$, is related to the local spin operator by S${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{i}}$=(1-${\mathit{e}}_{\mathit{i}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$
ei)
Si. The expression correctly produces the Nagaoka theorem in the limit J\ensuremath{\rightarrow}0, and preserves the time-reversal symmetry of the original model. For a bipartite lattice, H describes a competition between ferromagnetism, favored by the hopping term, and antiferromagnetism, favored by the Heisenberg term.
A new formulation of the many-electron correlation problem is presented based on the use of parastatistics. It is shown that second-order para-Fermi creation and annihilation operators, which correspond to the creation and annihilation of spin-averaged paraparticles, occur naturally for the spin-independent many-electron problem. Moreover, the spin-independent many-electron Hamiltonian is directly expressible in terms of the parafield operators. The structure of the general para-Fermi algebra is also investigated from the viewpoint of the pseudo-orthogonal group O(2n+1, 1). Finally, an explicit matrix representation for the para-Fermi algebra of order 2, which enables one to handle even particle-number-nonconserving operators, is obtained in a canonical U(n)-adapted basis.
We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class of non-canonical algebras also offer useful quantum degrees of freedom, allowing for the development of quasi-particle descriptions which go beyond the weakly correlated paradigm. We give a broad overview of such algebras for spin, electron and local moment systems, and outline important test problems upon which to develop the framework.