A devil's staircase in the Zeeman response of the 1D half-filled adiabatic Holstein model

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Abstract
The magnetization of the half-filled 1D adiabatic Holstein model in a magnetic field is investigated at 0 K. It has been proven elsewhere that at large enough electron-phonon coupling the ground state of this model with a large applied magnetic field is a mixed bipolaronic-polaronic configuration (at any band filling and at any dimension). In the half-filled case we propose as ground state for these polarons and bipolarons an ordered structure, which turns out to be equivalent to a periodic (or quasi-periodic) array of neutral solitons and which appears physically as spin density waves. We describe new improved numerical techniques for calculating these configurations and their energy. The magnetization as a function of the magnetic field is found to vary as a devil's staircase, each plateau corresponding to a commensurate array of neutral solitons. The first plateau corresponds to a structure with no neutral soliton, while the magnetic threshold field required to cross its edge corresponds to the energy of this neutral soliton. In analogy with the Frenkel-Kontorowa (FK) model this devil's staircase is believed to be incomplete if there is an analytic incommensurate array of neutral solitons (k<1.8), and complete otherwise. The magnetic threshold field required to observe the beginning of these devil's staircases could be accessible in real charge density waves, if their electronic gap (which is found to be about four times the energy of the neutral soliton) does not range beyond 100 K.