Condensed Matter

The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. Could this be different when the dissipation is engineered to drive the system into a nontrivial quantum coherent steady state? In this work we shed light on this issue by studying the effect of disorder on recently-introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite size scaling methods we show that the critical exponent ν describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the non-dissipative part of the dynamics. This indicates a different type of nonequilibrium quantum critical universality class accessible in cold-atom experiments.

In this paper we studied a one-dimensional array of quantum emitters asymmetrically coupled due to chiral interaction through a waveguiding mode. We have showed that disorder and coupling asymmetry compete with each other in forming and destroying Anderson localized states. We found that for wide range of the disorder strength there exists certain asymmetry parameter, which destroys the localization of the states. We have also numerically obtained the dependence of the critical asymmetry strength on the amplitude of the disorder. We believe that our findings are important for rapidly developing field of waveguide quantum electrodynamics, where the chiral interactions and disorder play a critical role.

We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been explored. In this work, we predict a disorder-induced topology of post-quench states characterized by the quantized dynamical Chern number and the crossings in the entanglement spectrum in (1+1) dimensions. The dynamical Chern number undergoes transitions from zero to unity, and back to zero when increasing the disorder strength. The boundaries between different dynamical Chern numbers are determined by delocalized critical points in the post-quench Hamiltonian with the strong disorder. An experimental realization in quantum walks is discussed.

The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the Haldane-Shastry model by allowing the spins to sit at random positions on the unit circle and study the properties of the eigenstates. At weak disorder, the spectrum is similar to the spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range interactions in the model do not decay as a simple power law. The eigenstates in the middle of the spectrum follow a volume law, but the coefficient is small, and the entropy is hence much less than for an ergodic system. In addition, the energy level spacing statistics is neither Poissonian nor of the Wigner-Dyson type. The behavior at strong disorder hence serves as an example of a non-ergodic phase, which is not of the many-body localized kind, in a model with long-range interactions and SU(2) symmetry.

Glasses, commonly formed by quickly cooling a liquid to avoid crystallization, feature a broad range of physical properties due to their diverse underlying disordered structures. Quantifying glassy disorder and understanding its range of variability are of prime importance, e.g.~for discovering structure-properties relations. In particular, it remains unknown whether minimally disordered glassy states exist and if so, whether the lower bound on glassy disorder might be universal. Here, using extensive computer simulations of various glass-forming liquids, we provide evidence for the existence of a generic lower bound on the degree of mesoscopic mechanical disorder -- quantified by elastic constants fluctuations -- of glasses formed by quenching a liquid. The degree of mesoscopic mechanical disorder is shown to follow a master curve in terms of the pre-factor of the universal ω 4 density of states of soft glassy excitations. Furthermore, our analysis suggests that the existence of minimally disordered glassy states is intimately related to the existence of a mesoscopic glassy length scale. These results pose fundamental questions about the nature of glasses and have implications for their properties, such as sound attenuation and heat transport.

We study a class of off-diagonal quasiperiodic hopping models described by one-dimensional Su-Schrieffer-Heeger chain with quasiperiodic modulations. We unveil a general dual-mapping relation in parameter space of the dimerization strength λ and the quasiperiodic modulation strength V , regardless of the specific details of the quasiperiodic modulation. Moreover, we demonstrated semi-analytically and numerically that under the specific quasiperiodic modulation, quantum criticality can emerge and persist in a wide parameter space. These unusual properties provides a distinctive paradigm compared with the diagonal quasiperiodic systems.

A mobility edge (ME) in energy separating extended from localized states is a central concept in understanding various fundamental phenomena like the metal-insulator transition in disordered systems. In one-dimensional quasiperiodic systems, there exist a few models with exact MEs, and these models are beneficial to provide exact understanding of ME physics. Here we investigate two widely studied models including exact MEs, one with an exponential hopping and one with a special form of incommensurate on-site potential. We analytically prove that the two models are mutually dual, and further give the numerical verification by calculating the inverse participation ratio and Husimi function. The exact MEs of the two models are also obtained by calculating the localization lengths and using the duality relations. Our result may provide insight into realizing and observing exact MEs in both theory and experiment.

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss how properties of the spectrum that are usually associated with chaos can be directly detected from the evolution of the number operator in the one-dimensional, noninteracting Aubry-André model. Both the quantity and the model are studied in experiments with cold atoms. We consider a single-particle and system sizes experimentally reachable. By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. This feature emerges at times that are experimentally accessible. This work is a contribution to a special issue dedicated to Shmuel Fishman.

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical p -spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

In the previous paper[arXiv:1911.02189], localization and delocalization phenomena in the polychromatically perturbed Anderson map (AM) were elucidated mainly from the viewpoint of localization-delocalization transition (LDT) on the increasing of the perturbation strength ϵ . In this paper, we mainly investigate the disorder strength W− dependence of the phenomena in the AM with a characetristic disorder strength W ∗ . In the completely localized region the W− dependence and ϵ− dependence of the localization length show characteristic behavior similar to those reported in monochromatically perturbed case [PRE 97,012210(2018)]. Furthermore, the obtained results show that even for the increase of the W , the critical phenomena and critical exponent are found to be similar to those in the LDT caused by the increase of ϵ . We also investigate the diffusive properties of the delocalized states induced by the parameters.