Phase diagram of an interacting staggered SuSchriefferHeeger twochain ladder close to a quantum critical point
Abstract
We study the groundstate phase diagram of an interacting staggered SuSchriefferHeeger (SSH) ladder in the vicinity of the Gaussian quantum critical point. The corresponding effective field theory is a doublefrequency sineGordon (DSG) model which involves two perturbations at the Gaussian fixed point: the deviation from criticality and Umklapp scattering processes. A topological distinction between thermodynamically equivalent phases becomes only feasible when nonlocal fermionic fields, parity and string order parameter, are included into consideration. We prove that a noninteracting fermionic staggered SSH ladder is exactly equivalent to a O(2)symmetric model of two decoupled KitaevMajorana chains, or two 1D pwave superconductors. Close to the Gaussian fixed point the SSH ladder maps to an AshkinTeller like system when interactions are included. Thus, the topological order in the SSH ladder is related to brokensymmetry phases of the associated quantum spinchain degrees of freedom. The obtained phase diagram includes a TomonagaLuttinger liquid state which, due to Umklapp processes, can become unstable against either spontaneous dimerization or the onset of a chargedensity wave (CDW). In these gapped phases elementary bulk excitations are quantum kinks carrying the charge QF = 1/2. For sufficiently strong, longrange interactions, the phase diagram of the model exhibits a bifurcation of the Gaussian critical point into two outgoing Ising criticalities. The latter sandwich a mixed phase in which dimerization coexists with a sitediagonal CDW. In this phase elementary bulk excitations are represented by two types of topological solitons carrying different fermionic charges, which continuously interpolate between 0 and 1. This phase has also mixed topological properties with coexisting parity and string order parameters.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.10380
 Bibcode:
 2020arXiv200510380N
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 19 pages, 5 figures. A few typos corrected, a minor amendment to the text, the version accepted by PRB