Competition and cancellation in a tilted Rice--Mele chain: exact Wannier--Stark offset and spectral readout

Abstract

In a tilted Rice--Mele chain, the Wannier--Stark (WS) ladder becomes staggered, \(E_n=n\Fo+(-1)^{n+1}A\). The offset \(A\) reflects the competition between the staggered onsite energy \(Δ\) and the dimerized hopping \(\dt\), and its cancellation restores spectral equidistance. We determine \(A\) through a systematic strong-field series in the WS basis and a nonperturbative two-band Floquet expression. An exact matrix element reduces the strong-field expansion to Bessel algebra; at the representative working point, truncation at seventh order locates the cancellation point with a theory-internal truncation error of \(0.010\)~Hz, against \(27.3\)~Hz at first order. The Floquet propagator gives the closed form \(A=(\Fo/π)\arcsin(-i\,\mathrm{Tr}\,U/2)\), exact within the two-band model, implying the kinematic bound \(|A|\le\Fo/2\) and identifying cancellation with maximum spectral uniformity. The same analytic structure yields a family of real zeros and complex exceptional points that set the convergence radius of the strong-field series without touching the real axis. On odd-length chains, the hidden-symmetry defect produces a pairing plateau of height \(2|A|\) that persists numerically beyond first order in the modulations, allowing the offset to be read from the static spectrum without Floquet propagation or time evolution. In the bulk, cancellation appears as the merging of two sidebands into a single line at \(\Fo\), a null measurement that requires no calibrated sideband amplitudes, although the tilt and line frequency still need calibration. These signatures provide complementary spectral tests of the staggered WS ladder and a calibration-aware route to precision force sensing.