Orthogonality Edges in Strong-Coupling Quantum Work Statistics

Abstract

Strong coupling to a reservoir can do more than shift, broaden, or dress the work peaks of a driven quantum system. When the reservoir is infrared singular, a sudden change of a local control parameter can alter the boundary condition seen by infinitely many low-energy modes, converting a quasiparticle-like threshold line into a many-body edge. We demonstrate this mechanism for the inclusive work distribution of the biased spin-boson model under a sudden bias inversion. In the independent-boson limit, the problem is exactly solvable and gives a sharp infrared classification: a super-Ohmic bath can retain a finite elastic threshold weight, whereas Ohmic and sub-Ohmic baths extinguish the elastic line through boundary orthogonality. At the Ohmic fixed point, the same exponent controls both the vanishing elastic residue and the low-work continuum. We then ask how this edge is resolved away from the static-boundary limit. Using displaced-basis exact diagonalization of logarithmically discretized baths, we find that finite tunnelling leaves an edge-like continuum over the accessible energy window, while separating two operational diagnostics of the threshold: the cumulative-continuum exponent extracted from $z$-interleaved spectra lies above the elastic-overlap exponent extracted from $z$-averaged overlaps, $θ_C>θ_Z$. We interpret this separation as a finite-energy crossover away from the static-boundary fixed point, not as evidence for a new asymptotic fixed point. The separation survives fitting-window variation, oscillator-cutoff checks, spectrum-size checks, and leave-one-$z$-out tests, while time-domain characteristic functions provide a compatible but non-decisive diagnostic. Finally, the same threshold edge controls the sampling cost of Jarzynski-type exponential averages, making rare low-work events increasingly important at low temperature.