We investigate the localization in a one-dimensional modified Peierls model with a non-adiabatic dynamic method. Different from the polaron scenario, here the localization stems from extensive conserved local quantities in the disorder-free lattice. Both the entanglement entropy and out-of-time-ordered correlator (OTOC) show the oscillating feature of dynamically generated localization. Although the strong interaction between electrons may suppress the dynamical features of the localization, but the effect of many-body localization is not observed. The role of disorder presented at finite temperature is discussed as well. The electrons diffuse in a classical manner. Benefitting from the indication of OTOC, it is found that the Anderson localization becomes dominant instead of dynamic localization as observed in disorder-free lattices.
We investigate the localization in a one-dimensional modified Peierls model with a non-adiabatic dynamic method. Different from the polaron scenario, here the localization stems from extensive conserved local quantities in the disorder-free lattice. Both the entanglement entropy and out-of-time-ordered correlator (OTOC) show the oscillating feature of dynamically generated localization. Although the strong interaction between electrons may suppress the dynamical features of the localization, but the effect of many-body localization is not observed. The role of disorder presented at finite temperature is discussed as well. The electrons diffuse in a classical manner. Benefitting from the indication of OTOC, it is found that the Anderson localization becomes dominant instead of dynamic localization as observed in disorder-free lattices.
Out-of-time-ordered correlators (OTOCs) describe information scrambling under unitary time evolution, and provide a useful probe of the emergence of quantum chaos. Here we calculate OTOCs for a model of disorder-free localization whose exact solubility allows us to study long-time behavior in large systems. Remarkably, we observe logarithmic spreading of correlations, qualitatively different to both thermalizing and Anderson localized systems. Rather, such behavior is normally taken as a signature of many-body localization, so that our findings for an essentially noninteracting model are surprising. We provide an explanation for this unusual behavior, and suggest a novel Loschmidt echo protocol as a probe of correlation spreading. We show that the logarithmic spreading of correlations probed by this protocol is a generic feature of localized systems, with or without interactions.
We investigate the quantum dynamics in a disordered electronic lattice by the time-dependent density matrix renormalization group algorithm. The on-site energy in the lattice follows the Fibonacci sequence and the electron off-diagonally couples to a sub-Ohmic phonon bath. It is found that the slope of the inverse participation ratio versus the coupling strength undergoes a sudden change that indicates a transition from static to dynamic localization, and that the generated polarons coherently diffuse via hopping-like processes, evidenced by the saturated entanglement entropy, providing a novel scenario for a transportation mechanism in strongly disordered systems. Moreover, the mean-square displacement is revealed to be insensitive to the coupling strength, implying the quantum diffusion behavior survives the energy disorder that prevails in real organic materials.
The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.
Anderson localization, where quenched disorder leads to the localization of single-particle wave functions, has been studied extensively. However, the effect of interaction and non-random potentials on many-body localization (MBL) has gained attention recently. We investigate the dynamics of the interacting Aubry-André model to assess the stability of the many-body localized (MBL) phase. Our motivation to consider the Aubry–André potential as the disorder potential is to eliminate the avalanche mechanism, which often destabilizes MBL in systems with quenched disorder. We analyze the time evolution and the system-size scaling across a range of disorder strengths for the entanglement entropy, number entropy, and the Hartley number entropy. In the non-interacting case, our results confirm an Anderson localization transition at a critical disorder strength Dc = 2, which is consistent with earlier studies. However, when interactions are introduced, the number entropy appears to grow unboundedly as SN ~ ln ln t in the thermodynamic limit, even for large disorder. Meanwhile, the entanglement entropy grows logarithmically, S ~ ln t, and both entropies saturate in a correlated manner at finite times td ~ e^(L·D). These findings suggest that using a quasiperiodic potential to remove the avalanche mechanism does not stabilize true MBL behavior. Instead, the long-time dynamics are qualitatively similar to those found in systems with random disorder. In this thesis, we first introduce the fundamental concepts of thermalization, quantum quench, and symmetry-resolved entropies, then provide a study of localization, specifically in the Aubry-André model. Finally, we place our numerical results in the broader context of the current debate on the stability of many-body localized phases.
Many-body localization of a disorder interacting boson system in one dimension is studied numerically at the filling factor being one-half, in terms of level statistics, local compressibility, correlation function and entanglement entropies. The von Neumann entanglement entropy is decoupled into a particle number entropy and a configuration entropy. An anomalous volume-law behavior is found for the configuration entanglement entropy to confirm a recent experimental observation [A. Lukin, M. Rispoli, R. Schittko, et al., Science 364, 256 (2019)] for sufficient strong disorder, while the particle number entropy fulfills an area-law corresponding to the total entropy for disordered spin chain. The localization length are extracted from a two-body correlation function for many-body localization states and corresponding time-evolutions states as well. A phase diagrams is established with consisting of an ergodic thermalized region and a many-body-localization region in a parameter space of the disorder strength and the energy density. Two regions are separated by a many-body mobility edge deducted from the standard deviation of the particle-number entanglement entropy, which appears consistent with that based on the localization length. Slow dynamics characterized by a logarithmic time-dependence is explicitly shown for both the particle number entropy and the configuration entropy in an intermediate regime of their time-evolutions, which does not show up in the Anderson localization case, i.e. non-interacting disorder systems.
Different from traditional semiconductors, the organic semiconductors normally possess moderate many-body interactions with respect to charge, exciton, spin and phonons. In particular, the diagonal electron-phonon couplings give rise to the spatial localization and the off-diagonal couplings refer to the delocalization. With the competition between them, the electrons are dispersive in a finite extent and unfavorable towards thermal equilibrium. In this context, the quantities from the statistical mechanics such as the entropy have to be reexamined. In order to bridge the localization-delocalization duality and the device performance in organic semiconductors, the quantum heat engine model is employed to describe the charge, exciton and spin dynamics. We adopt the adaptive time-dependent density matrix renormalization group algorithm to calculate the time evolution of the out-of-time-ordered correlator (OTOC), a quantum dynamic measurement of the entanglement entropy, in three models with two kinds of competing many-body interactions: two-bath lattice model with a single electron, Frenkel-charge transfer mixed model, and the Merrifield model for singlet fission. We respectively investigate the parameter regime that the system is in the many-body localization (MBL) phase indicated by the behavior of OTOC. It is recognized that the novel effects of coherent electron hopping, the ultrafast charge separation and the dissociation of triplet pairs are closely related to the MBL effect. Our investigation unifies the intrinsic mechanisms correlating to charge, exciton and spin into a single framework of quantum entanglement entropy, which may help clarify the complicated and diverse phenomena in organic semiconductors.