Physical manifestation of replica symmetry breaking in a quantum glass of bosons with off-diagonal disorder

Glassiness occurs when disorder and frustration cause local degrees of freedom to freeze despite the lack of long-range order. In systems of interacting bosons, such glassiness may involve a purely quantum degree of freedom$\text{unicode}x2014$local phases of particle wave functions$\text{unicode}x2014$partly analogous to spins in spin glasses. However, experimental identification of such phases is difficult because it requires prohibitively long measurement times or recourse to the elusive Edwards-Anderson order parameter. Moreover, the off-diagonal character of the phase makes it seemingly even harder to capture via typical observables. To address this issue, we study a system of strongly interacting bosons with random hoppings that features off-diagonal glassiness exhibiting replica symmetry breaking (RSB). We find that the glass phase is compressible, which distinguishes it from the Mott insulator. Thus, we establish a direct correspondence between phase-based glassy order and a measurable density-based thermodynamic observable. We use a framework adopted from spin glasses, including the replica trick within the one-step RSB scheme, to obtain meaningful results in the glass phase and to characterize the order parameters, RSB structure, slow relaxation, and compressibility. Glassiness in particle systems could thus be experimentally identified via measurements of compressibility, such as probing density fluctuations or the particle-number response to a trapping potential.