We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent sign-alternating potentials. In a continuum description, the latter supply the fermions with spin-dependent relativistic masses $m_{\uparrow ,\downarrow }$. The ground-state phase diagram describes three gapped phases: the charge-density-wave (CDW) and spin-density-wave (SDW)-like band insulator phases sandwiched by a mixed phase in which the CDW and SDW superstructures coexist with a nonzero spontaneous dimerization (SD). The critical lines separating the massive phases belong to the Ising universality class. The Ising criticality is accompanied by the Kohn anomaly in the renormalized phonon spectrum. We derive a Ginzburg criterion which specifies a narrow region around the critical point where quantum fluctuations play a dominant role, rendering the adiabatic (or mean-field) approximation inapplicable. A full account of quantum effects is achieved in the antiadiabatic limit where the effective low-energy theory represents a massive version the $N=4$ Gross-Neveu model. Using Abelian bosonization, we demonstrate that the description of the SD phase, including its critical boundaries, is well approximated by a sum of two effective double-frequency sine-Gordon (DSG) models subject to self-consistency conditions that couple the charge and spin sectors. Using the well-known critical properties of the DSG model, we obtain the singular parts of the dimerization order parameter and staggered charge and spin susceptibilities near the Ising critical lines. We show that, in the antiadiabatic limit, on the line $m_{\downarrow }=0$ there exists of a Berezinskii-Kosterlitz-Thouless critical point separating a Luttinger-liquid gapless phase from the spontaneously dimerized one. We also discuss topological excitations of the model carrying fractional charge and spin.

• Received 13 November 2018
• Revised 4 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.035134