Quench Spectroscopy of a Disordered Quantum System

Finding the phase diagram of strongly-correlated disordered bosons using quantum quenches

“…The former partially overlaps with and complements the discussion of Ref. [1]. We work in the grand canonical ensemble and explore the regime where J, ∆ U .…”

“…IV we present numerical results for the disordered Bose-Hubbard chain, comparing several observables and expanding upon the results of Ref. [1]. We discuss how different observables probe distinct spectral properties, which can be used to describe various features of the elementary excitations within each phase, and enables direct measurement of the speed of sound in the superfluid phase.…”

“…An additional strong contribution close to k = 0 for frequencies ω > 0, caused by the sensitivity of the one-body correlator to the quasi-long-range order in the system, leads to a V-shaped continuum around k = 0. Nonetheless, the lower edge of this continuum is linear close to k = 0, with a gradient equal to the sound velocity [1], as indicated by the cyan line in Fig. 3.…”

“…This can be established in two ways: firstly by examining the zero-frequency amplitude of |G(k = 0, ω = 0)| as a function of ∆/J and U f /J (as used in Ref. [1]), and secondly by directly extracting the excitation gap itself E gap (∆) (indicated in Fig. 4, and by the solid dark blue line in Fig.…”

“…In Ref. [1], we have shown that quench spectroscopy can be extended to disordered systems, and is able to distinguish between all three zero-temperature phases of the disordered Bose-Hubbard model. Moreover, we have introduced a new local probe which provides information on the spatial distribution of gapped and gapless regions, acting as an alternative probe of the various phases.…”