Generation of topological phases of matter with SU(3) symmetry in a condensed matter setup is challenging due to the lack of an intrinsic three-fold chirality of quasiparticles. We uncover two salient ingredients required to express a three-component lattice Hamiltonian in a SU(3) format with non-trivial topological invariant. We find that all three SU(3) components must be entangled via a gauge field, with opposite chirality between any two components, and there must be band inversions between all three components in a given eigenstate. For spinless particles, we show that such chiral states can be obtained in a tripartite lattice with three inequivalent lattice sites in which the Bloch phase associated with the nearest neighbor hopping acts as k-space gauge field. The second and a more crucial criterion is that there must also be an odd-parity Zeeman-like term, i.e. sin(k)σz term where σz is the third Pauli matrix defined in any two components of the SU(3) basis. Solving the electron-photon interaction term in a periodic potential with a modified tight-binding model, we show that such a term can be engineered with site-selective photon polarization. Such site selective polarization can be obtained in multiple ways, such as using Sisyphus cooling technique, polarizer plates, etc. With the k-resolved Berry curvature formalism, we delineate the relationship between the SU(3) chirality, band inversion, and k-space monopoles, governing finite Chern number without breaking the time-reversal symmetry. The topological phase is affirmed by edge state calculation, obeying the bulk-boundary correspondence.
We study the effect of a boost (Fermi sea displaced by a finite momentum) on one dimensional systems of lattice fermions with short-ranged interactions. In the absence of a boost such systems with attractive interactions possess algebraic superconducting order. Motivated by physics in higher dimensions, one might naively expect a boost to weaken and ultimately destroy superconductivity. However, we show that for one dimensional systems the effect of the boost can be to strengthen the algebraic superconducting order by making correlation functions fall off more slowly with distance. This phenomenon can manifest in interesting ways, for example, a boost can produce a LutherEmery phase in a system with both charge and spin gaps by engendering the destruction of the former.
The purpose of this paper is to give a physical interpretation of all the Henon integrals of motion of the CSM model in the limit of small excitation energies. These integrals are first evaluated for the lattice at rest. It is then proved that the harmonic approximations of the Henon constants are integrals of motion of the harmonic CSM model and that they can be expressed as linear combinations of the action variables of the harmonic lattice. Moreover a method of calculation of the coefficients of these linear combinations is presented and illustrated.
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