Bound-States Dynamics in One-Dimensional Multi-Species Fermionic Systems

Abstract

In this work we provide for a description of the low-energy physics of interacting multi-species fermions in terms of the bound-states that are stabilized in these systems when a spin gap opens. We argue that, at energies much smaller than the spin gap, these systems are described by a Luttinger liquid of bound-states that depends, on top of the charge stiffness $\nu$ and the charge velocity $u$, on a "Fermi" momentum $P_F$ satisfying $q{P}_F=N{k}_F$ where $q$ is the charge of the bound-state, $N$ the number of species and $k_F$ is the Fermi momentum in the non-interacting limit. We further argue that for generic interactions, generic bound-states are likely to be stabilized. They are associated with emergent, in general non-local, symmetries and are in the number of five. The first two consist of either a charge $q=N$ local $SU(N)$ singlet or a charge $q=N$ bound-state made of two local $SU(p)$ and $SU(N-p)$ singlets. In this case the Fermi momentum $P_F=k_F$ is preserved. The three others have an enhanced Fermi vector $P_F$. The latter are either charge $q=2$ bosonic p-wave and s-wave pairs with $SO(N)$ and $SP(N)$ symmetry and $P_F=N{k}_F/2$ or a composite fermion of charge $q=1$ with $P_F=N{k}_F$. The instabilities of these Luttinger liquid states towards incompressible phases and their possible topological nature are also discussed.

46 Pages

References in corpus (11)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Rise and fall of hidden string order of lattice bosons
• Competing orders in one dimensional spin 3/2 fermionic systems
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap
• Confinement vs Deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms
• Three-Component Fermi Gas in a one-dimensional Optical Lattice
• Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture
• General method for calculating the universal conductance of strongly correlated junctions of multiple quantum wires
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach

Cited by in corpus (3)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• From one-dimensional charge conserving superconductors to the gapless Haldane phase
• Interplay between intrinsic and emergent topological protection on interacting helical modes