Magnetic-field and chemical-potential effects on the low-energy separation

摘要

We show that in the presence of a magnetic field the usual low-energyseparation of the Hubbard chain is replaced by a ``$c$'' and ``$s$''separation. Here $c$ and $s$ refer to small-momentum and low-energy independentexcitation modes which couple both to charge and spin. Importantly, we find theexact generators of these excitations both in the electronic and pseudoparticlebasis. In the limit of zero magnetic field these generators become the usualcharge and spin fluctuation operators. The $c$ and $s$ elementary excitationsare associated with the $c$ and $s$ pseudoparticles, respectively. We alsostudy the separate pseudoparticle left and right conservation laws. In thepresence of the magnetic field the small-momentum and low-energy excitationscan be bosonized. However, the suitable bosonization corresponds to the $c$ and$s$ pseudoparticle modes and not to the usual charge and spin fluctuations. Weevaluate exactly the commutator between the electronic-density operators. Itsspin-dependent factor is in general non diagonal and depends on theinteraction. The associate bosonic commutation relations characterize thepresent unconventional low-energy separation.