A New Model for Heat Transport in Low-dimensional Systems

Low-dimensional materials have become an important venue for studying strongly correlated and topological physics over the past decade. While much attention has been paid to electronic degrees of freedom, the atomic degrees of freedom, to our knowledge, have not been studied as extensively. We start with the following question: In low dimensional systems, is phonon still a good description of vibrational modes of atomic degrees of freedom? We exploit the fact that the atoms near the surface of a bulk system, or in an intrinsically low-dimensional system, are under suppressed oscillations in the direction perpendicular to the boundary. We develop a technique to phenomenologically achieve the suppression of vibration amplitudes by a restriction of the dimension of the Hilbert space for each atom. As a toy model, we first map a 1D harmonic chain, with atomic vibrations restricted along its perpendicular direction, to a two-band fermionic model with a novel continuous symmetry and various discrete symmetries. Anharmonic terms could then be mapped to 4-Fermion interactions, generating a novel type of interacting fermionic model with non-trivial symmetries. Effects of such restricted geometries on the transport properties of low-dimensional systems will be discussed.