Exact SO(8) Symmetry in the Weakly-Interacting Two-Leg Ladder

TL;DR

This paper demonstrates that a weakly-interacting two-leg ladder at half-filling exhibits an exact SO(8) symmetry, allowing for precise characterization of its ground state, excitations, and phases, including a Mott insulator and various phases with distinct symmetries.

Contribution

It reveals an exact SO(8) symmetry in the weakly-interacting two-leg ladder and provides detailed spectra and phase structure at half-filling, including all low-energy multiplets.

Findings

Ground state is a Mott insulator with short-range d-wave correlations.

Exact energies, degeneracies, and quantum numbers of all low-energy multiplets are obtained.

Identifies five robust phases with distinct SO(8) symmetries sharing an SO(5) subgroup.

Abstract

A perturbative renormalization group analysis of interacting electrons on a two-leg ladder reveals that at half-filling any weakly repulsive system scales onto an exactly soluble Gross-Neveu model with a hidden SO(8) symmetry. The half-filled ground state is a Mott insulator with short-range d-wave pair correlations. We extract the exact energies, degeneracies, and quantum numbers of *all* the low energy excited multiplets. One energy (mass) m octets contains Cooper pair, magnon, and density-wave excitations, two more octets contain single-particle excitations, and a mass \sqrt{3}m antisymmetric tensor contains 28 "bound states". Exact single-particle and spin gaps are found for the lightly-doped (d-wave paired one-dimension Bose fluid) system. We also determine the four other robust phases occuring at half-filling for partially attractive interactions. All 5 phases have distinct SO(8) symmetries, but share S.C. Zhang's SO(5) as a common subgroup.