Topology and the one-dimensional Kondo-Heisenberg model

Abstract

The Kondo-Heinsberg chain is an interesting model of a strongly correlated system which has a broad superconducting state with pair-density wave (PDW) order. Some of us have recently proposed that this PDW state is a symmetry-protected topological (SPT) state, and the gapped spin sector of the model supports Majorana zero modes. In this work, we reexamine this problem using a combination of numeric and analytic methods. In extensive density matrix renormalization group calculations, we find no evidence of a topological ground state degeneracy or the previously proposed Majorana zero modes in the PDW phase of this model. This result motivated us to reexamine the original arguments for the existence of the Majorana zero modes. A careful analysis of the effective continuum field theory of the model shows that the Hilbert space of the spin sector of the theory does not contain any single Majorana fermion excitations. This analysis shows that the PDW state of the doped 1D Kondo-Heisenberg model is not an SPT with Majorana zero modes. arXiv:2002.01483v1 [cond-mat.str-el]

Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder

“…Despite this entanglement transition, we believe the system does not have a true phase transition. Also, we do not find any boundary states at zero energy with open boundary for J K < J c K , consistent with the earlier discovery that the PDW is not topological 20 . Entanglement transition without boundary mode and true phase transition has also been reported in a different model 28 .…”

“…Unlike previous studies which dope both legs 17 , in our case only one leg is doped due to orbital or layer selective Mott localization caused by potential difference. Finally, we note that a PDW phase with Q = π was previously reported in a Kondo-Heisenberg model with the Heisenberg coupling J = 2t [18][19][20] . Such a model resembles our generalized Kondo model with J K > 0.…”