Competing phases and critical phenomena in three coupled spinless Luttinger liquids

Coupled one-dimensional systems of interacting fermions appear in diverse contexts, and bosonization, along with a scaling treatment, is the usual method for studying low-energy properties of such systems. If three or more fermionic species are present, the scaling procedure generically introduces off-diagonal corrections to the stiffness matrix in the quadratic part of the bosonized Hamiltonian, requiring both rescaling as well as large rotations of the fields. In this talk, I will discuss phase competition in a system of three coupled spinless Luttinger liquids, using bosonization, along with a renormalization group analysis which takes into account these rotations, generating a coupling between different interaction channels even at the tree-level order in the coupling constants. I will further discuss the different instabilities in the particle-particle and particle-hole channels, the nature of the phase transitions, and the conditions under which valley symmetry breaking and intervalley orders may appear. These results may be directly relevant for systems with multiple small Fermi pockets (like graphite intercalates and bismuth) subject to quantizing magnetic fields, and cylindrical nanotubes at high fields.