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

TL;DR

This paper demonstrates that a magnetic field alters the low-energy excitation separation in the Hubbard chain, revealing new 'c' and 's' modes linked to pseudoparticles, with exact generators and unconventional bosonization.

Contribution

It introduces the concept of 'c' and 's' low-energy modes in a magnetic field, providing exact generators and a novel bosonization approach based on pseudoparticles.

Findings

Exact generators for 'c' and 's' excitations are derived.

Bosonization corresponds to pseudoparticle modes, not traditional charge/spin modes.

The electronic-density commutator has a non-diagonal, interaction-dependent spin factor.

Abstract

We show that in the presence of a magnetic field the usual low-energy separation of the Hubbard chain is replaced by a ``$c$'' and ``$s$'' separation. Here $c$ and $s$ refer to small-momentum and low-energy independent excitation modes which couple both to charge and spin. Importantly, we find the exact generators of these excitations both in the electronic and pseudoparticle basis. In the limit of zero magnetic field these generators become the usual charge and spin fluctuation operators. The $c$ and $s$ elementary excitations are associated with the $c$ and $s$ pseudoparticles, respectively. We also study the separate pseudoparticle left and right conservation laws. In the presence of the magnetic field the small-momentum and low-energy excitations can be bosonized. However, the suitable bosonization corresponds to the $c$ and $s$ pseudoparticle modes and not to the usual charge and spin fluctuations. We evaluate exactly the commutator between the electronic-density operators. Its spin-dependent factor is in general non diagonal and depends on the interaction. The associate bosonic commutation relations characterize the present unconventional low-energy separation.