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

Abstract

The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In Ref.[1], we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here, we extend this work by providing a more in-depth study of the behavior of the quench spectral functions associated to different observables and investigating an extended parameter regime. We provide a detailed introduction to quench spectroscopy for disordered systems and show how spectral properties can be probed using both local operators and two-point correlation functions. We benchmark the technique using the one-dimensional Bose-Hubbard model in the presence of a random external potential, focusing on the low-lying excitations, and demonstrate that quench spectroscopy can distinguish the Mott insulator, superfluid, and Bose glass phases. We then explicitly reconstruct the zero-temperature phase diagram of the disordered Bose-Hubbard at fixed filling using two independent methods, both experimentally accessible via time-of-flight imaging and quantum gas microscopy respectively, and demonstrate that quench spectroscopy can give valuable insights as to the distribution of rare regions within disordered systems.

Emergence of damped-localized excitations of the Mott state due to disorder

“…We point out that the spectral function can experimentally be determined, for instance by Bragg spectroscopy [55,56] or by the radio frequency transfer method [57]. Moreover, it has been recently proposed that the spectral function could be used to probe key aspects of the excitation spectrum in the disordered case in quench spectroscopy experiments [58,59]. Further insight into the transition to the superfluid phase could be obtained by including loop corrections to the resummation method developed here.…”

Late-time critical behavior of local string-like observables under quantum quenches

“…Even so, it is usually difficult to understand how equilibrium critical phenomena can manifest in generic high energy excited states of a system. In this light, there has been an extensive search for footprints of quantum criticality in excited and particularly out of * souvik@iitk.ac.in equilibrium systems [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Particularly, Ref.…”