We find a unitary operator which asymptotically diagonalizes the Tomonaga-Luttinger Hamiltonian of one-dimensional spinless electrons. The operator performs a Bogoliubov rotation in the space of electron-hole pairs. If bare interaction of the physical electrons is sufficiently small this transformation maps the original Tomonaga-Luttinger system on a system of free fermionic quasiparticles. Our representation is useful when the electron dispersion deviates from linear form. For such situation we obtain non-perturbative results for the electron gas free energy and the density-density propagator.
European Physical Journal B
- Pub Date:
- September 2005
- Fermions in reduced dimensions;
- Condensed Matter - Strongly Correlated Electrons
- In the new version two new appendices are added, several errors and misprints are corrected