The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here we show that quench spectroscopy of a disordered model, as realized from its out-of-equilibrium dynamics following a global quench, allows us to fully characterize the spectral properties of the disordered phases. In the Bose-Hubbard model, a clear signature of gapless excitations in momentum-resolved spectroscopy enables us to accurately locate the Mott insulator to Bose glass transition, while the presence or absence of a well-defined soundlike mode distinguishes the superfluid from the Bose glass phase. Moreover, spatially resolved spectroscopy provides local spectral properties and allows us to extract the typical spacing of gapless regions, giving a second independent way to uniquely identify all three phases. Our findings have far-ranging implications for a variety of experimental platforms and offer a powerful and versatile probe of the low-energy phases of disordered systems.
The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here we show that quench spectroscopy of a disordered model, as realized from its out-of-equilibrium dynamics following a global quench, allows us to fully characterize the spectral properties of the disordered phases. In the Bose-Hubbard model, a clear signature of gapless excitations in momentum-resolved spectroscopy enables us to accurately locate the Mott insulator to Bose glass transition, while the presence or absence of a well-defined soundlike mode distinguishes the superfluid from the Bose glass phase. Moreover, spatially resolved spectroscopy provides local spectral properties and allows us to extract the typical spacing of gapless regions, giving a second independent way to uniquely identify all three phases. Our findings have far-ranging implications for a variety of experimental platforms and offer a powerful and versatile probe of the low-energy phases of disordered systems.
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 the preceding Letter [L. Villa, S. J. Thomson, and L. Sanchez-Palencia, preceding Letter, Phys. Rev. A 104, L021301 (2021)] 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 with 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, experimentally accessible via both time-of-flight imaging and quantum gas microscopy, respectively, and demonstrate that quench spectroscopy can give valuable insights into the distribution of rare regions within disordered systems.
Quench spectroscopy is a relatively new method which enables the investigation of spectral properties of many-body quantum systems by monitoring the out-of-equilibrium dynamics of real-space observables after a quench. So far the approach has been devised for global quenches or using local engineering of momentum-resolved excitations. Here, we extend the quench spectroscopy method to local quenches. We show that it allows us to extract quantitative information about global properties of the system, and in particular the elementary excitation spectrum. Using state-of-the-art numerical methods, we simulate the out-of-equilibrium dynamics of a variety of quantum systems following various local quench protocols and demonstrate a general scheme for designing an appropriate local quench protocol for any chosen model. We provide detailed examples of how the local quench protocol can be realized in realistic current generation experiments, including ultracold atomic gases and trapped ion systems.
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
We study the dynamic structure factor of a one-dimensional Bose gas confined in an optical lattice and modeled by the Bose–Hubbard Hamiltonian, using a variety of numerical and analytical approaches. The dynamic structure factor, experimentally measurable by Bragg spectroscopy, is studied in three relevant cases: in the clean regime, featuring either a superfluid or a Mott phase; and in the presence of two types of (quasi-)disordered external potentials: a quasi-periodic potential obtained from a bichromatic superlattice and a random box disorder—both featuring a Bose-glass phase. In the clean case, we show the emergence of a gapped doublon mode (corresponding to a repulsively bound state) for incommensurate filling, well separated from the low-energy acoustic mode. In the disordered case, we show that the dynamic structure factor provides direct insight into the spatial structure of the excitations, unveiling their localized nature, which represents a fundamental signature of the Bose-glass phase. Furthermore, it provides a clear fingerprint of the very nature of the localization mechanism which differs for the two kinds of disorder potentials we consider. In special cases, the dynamic structure factor may provide an estimate of the position of the localization transition from superfluid to Bose glass, in a complementary manner to the information deduced from the momentum distribution.
In this work, we characterize the glassy character of the Bose-glass phase in a disordered Bose-Hubbard model using three complementary diagnostics: the finite-temperature spectral function, spatial inhomogeneity, and the inverse participation ratio. Spectral analysis, obtained from finite-temperature Green's function and random phase approximation, shows that disorder introduces localized low-energy states within the Mott gap, eventually closing the gap at sufficiently strong disorder. Spatial inhomogeneity, calculated using the Gutzwiller ansatz, increases sharply with disorder and then saturates at moderate disorder strengths. The inverse participation ratio has been calculated from the exact diagonalization of a small system, and it reveals enhanced localization with stronger disorder. Increasing temperature suppresses these disorder-induced features: the low-energy spectral weight diminishes, the spatial inhomogeneity varies more smoothly, and the IPR decreases. Taken together, these diagnostics show that disorder drives the development of glassy character, while thermal fluctuations gradually wash out its signatures. The early saturation of spatial inhomogeneity compared with the continued evolution of low-energy excitations and the inverse participation ratio demonstrates that no single diagnostic fully captures the evolution of the Bose-glass state, highlighting the need for a combined characterization.
We numerically investigate the two-dimensional Bose-Hubbard model with local onsite disorder, where the competition between disorder and short-range interactions leads to the emergence of a Bose glass (BG) phase between the Mott insulator (MI) and superfluid (SF) phases. In order to analyze the inhomogeneous system we employ real-space bosonic dynamical mean-field theory (RBDMFT) and perform an ensemble average over disorder realizations. To distinguish the MI from the BG phase, we compare the Edwards-Anderson order parameter and the compressibility with the energy-gap condition. To identify the insulator to SF transition, we apply a percolation analysis to the condensate order parameter. In qualitative accordance with the theorem of inclusions we always find an intermediate BG phase between the SF and MI. However, the quantitative comparison indicates significant deviations between the MI to BG phase boundary expected in the thermodynamic limit and the one obtained for a finite system size. Additionally, RBMDFT is capable of reliably calculating spectral information throughout the phase diagram. Analyzing the spectral function reveals evidence for analytically predicted damped localized modes in the dispersion relation in the strong-coupling regime.