We systematically study the effect of disorder and interactions on a quasi-one-dimensional diamond chain possessing flat bands.Disorder localizes all the single-particle eigenstates, while at low disorder strengths, we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL).The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wave-packet dynamics.For low disorder, a damped oscillatory recurrence behavior is observed which is absent for high disorder.Noninteracting many-particle fermion states also follow the same trend except showing a delocalizing tendency at intermediate disorder due to the fermionic statistics in the system.As interactions are switched on, for the finite sizes that we are able to study, a nonergodic "mixed phase" is observed at low disorder which is separated from the MBL phase at high disorder by a thermal phase at intermediate disorder.A study of many-body nonequilibrium dynamics reinforces these findings.
We systematically study the effect of disorder and interactions on a quasi-one-dimensional diamond chain possessing flat bands.Disorder localizes all the single-particle eigenstates, while at low disorder strengths, we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL).The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wave-packet dynamics.For low disorder, a damped oscillatory recurrence behavior is observed which is absent for high disorder.Noninteracting many-particle fermion states also follow the same trend except showing a delocalizing tendency at intermediate disorder due to the fermionic statistics in the system.As interactions are switched on, for the finite sizes that we are able to study, a nonergodic "mixed phase" is observed at low disorder which is separated from the MBL phase at high disorder by a thermal phase at intermediate disorder.A study of many-body nonequilibrium dynamics reinforces these findings.
We study the effects of quasiperiodic Aubry-Andr\'e (AA) disorder and interactions on a one-dimensional all-bands-flat (ABF) diamond chain. We consider the application of disorder in two ways: A symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell, and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. The single-particle wave-packet dynamics for the clean system and when the disorder is applied symmetrically show quantum caging; in the antisymmetric case, the wave packet spreads over the entire lattice. These results agree with our previous study, where compact localization was observed in the case of the clean system and for symmetrically disordered diamond lattices. In the presence of nearest-neighbor interactions, nonergodic phases are observed in the case of a clean system and symmetrical disorder; at higher disorder strengths, we find an MBL-like phase in the symmetric case. However, many-body nonequilibrium dynamics of the system from carefully engineered initial states exhibit quantum caging. In the antisymmetric case, a nonergodic mixed phase, a thermal phase, and an MBL-like phases, respectively, are observed at low, intermediate, and high disorder strengths. We observe an absence of caging and initial state dependence (except at the intermediate disorder strength) in the study of nonequilibrium dynamics.
We clarify the interplay and competition between disorder and flat band in the Creutz ladder with interparticle interactions focusing on the system's dynamics. Without disorder, the Creutz ladder exhibits flat-band many-body localization (FMBL). In this work, we find that disorder generates drastic effects on the system, i.e., addition of it induces a thermal phase first and further increase of it leads the system to the conventional many-body-localized (MBL) phase. The competition gives novel localization properties and unconventional quench dynamics to the system. We first draw the global sketch of the localization phase diagram by focusing on the two-particle system. The thermal phase intrudes between the FMBL and MBL phases, the regime of which depends on the strength of disorder and interactions. Based on the two-particle phase diagram and the properties of the quench dynamics, we further investigate finite-filling cases in detail. At finite-filling fractions, we again find that the interplay and competition between the interactions and disorder in the original flat-band Creutz ladder induces a thermal phase, which separates the FMBL and MBL phases. We also verify that the time evolution of the system coincides with the static phase diagrams. For suitable fillings, the conservation of the initial-state information and low-growth entanglement dynamics are also observed. These properties depend on the strength of disorder and interactions.
The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with transverse hopping that possesses such stable flat bands and show that many-body localization appears in the presence of interactions without quenched disorder. We numerically demonstrate that the eigenstate thermalization hypothesis is violated. We show that the influence of degenerate flat band states spreads across the full energy spectrum and grows extensively in the thermodynamic limit. Furthermore, we verify localization in terms of time evolution of some local observable, revival probability, participation ratio, and entanglement entropy.
Abstract We study the broadening of initially localized wave packets in a quasi one-dimensional diamond ladder with interacting, spinless fermions. The lattice possesses a flat band causing localization. We place special focus on the transition away from the flat band many-body localized case by adding very weak dispersion. By doing so, we allow propagation of the wave packet on significantly different timescales which causes anomalous diffusion. Due to the temporal separation of dynamic processes, an interaction-induced, prethermal equilibrium becomes apparent. A physical picture of light and heavy modes for this prethermal behavior can be obtained within Born–Oppenheimer approximation via basis transformation of the original Hamiltonian. This reveals a detachment between light, symmetric and heavy, anti-symmetric particle species. We show that the prethermal state is characterized by heavy particles binding together mediated by the light particles.
We study the $t\text{\ensuremath{-}}V$ disordered spinless fermionic chain in the strong-coupling regime, $t/V\ensuremath{\rightarrow}0$. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: blocks with only one mover and ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show a many-body localized (MBL) transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe subdiffusive dynamics at finite timescales and find indications that this might be only a transient behavior before crossing over to diffusion.
We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple two- and four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.