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

Abstract

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 is a double-frequency sine-Gordon (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 Kitaev-Majorana chains, or two 1D 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 which, 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.

19 pages, 5 figures. A few typos corrected, a minor amendment to the text, the version accepted by PRB

References in corpus (5)

• Rise and fall of hidden string order of lattice bosons
• Topological orbital ladders
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Topological phases and quantum computation
• Possible quantum phase-manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms

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• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Quantum Restored Symmetry Protected Topological Phases
• Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings
• Tunable zero modes and quantum interferences in flat-band topological insulators