Phase diagram of an interacting staggered Su-Schrieffer-Heeger two-chain ladder close to a quantum critical point

• Published in: Physical review. B 2020-07, Vol.102 (4), p.1, Article 045108
• Main Author: Nersesyan, A. A.
• Format: Article
• Language: English
• Subjects: Bifurcations; Broken symmetry; Bulk density; Chains; Charge density waves; Critical point; Current carriers; Dimerization; Equivalence; Excitation; Field theory; Ising model; Mathematical models; Order parameters; P waves; Parameter identification; Parity; Phase diagrams; Phases; Solitary waves; Strings; Symmetry; Topology
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.102.045108

We study the ground-state phase diagram of an interacting staggered Su-Schrieffer-Heeger (SSH) ladder in the vicinity of the Gaussian quantum critical point. The corresponding effective field theory, which nonperturbatively treats correlation effects in the ladder, is a double-frequency sine-Gordon (DSG) model. It involves two perturbations at the Gaussian fixed point: the deviation from criticality, and umklapp scattering processes. While massive phases with broken symmetries are identified by means of local order parameters, a topological distinction between thermodynamically equivalent phases becomes feasible only when nonlocal fermionic fields, parity, and the string order parameter are included in consideration. We prove that a noninteracting fermionic staggered SSH ladder is exactly equivalent to an O(2)-symmetric model of two decoupled Kitaev-Majorana chains, or two one-dimensional p-wave superconductors. Close to the Gaussian fixed point, the SSH ladder maps to an Ashkin-Teller-like system when interactions are included. Thus, the topological order in the SSH ladder is related to broken-symmetry phases of the associated quantum spin-chain degrees of freedom. The obtained phase diagram includes a Tomonaga-Luttinger liquid state that, due to umklapp processes, can become unstable against either spontaneous dimerization or the onset of a charge-density wave (CDW). In these gapped phases, elementary bulk excitations are quantum kinks carrying the charge QF = 1/2. For sufficiently strong, long-range 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 site-diagonal 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.