Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single-particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two--body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.
Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single-particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two--body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.
We generate translationally invariant systems exhibiting many-body localization from all-bands-flat single-particle lattice Hamiltonians dressed with suitable short-range many-body interactions. This phenomenon, dubbed many-body flatband localization, is based on symmetries of both single-particle and interaction terms in the Hamiltonian, and it holds for any interaction strength. We propose a generator of corresponding Hamiltonians which covers both interacting bosons and fermions for arbitrary lattice dimensions, and we provide explicit examples of such models in one and two lattice dimensions. We also explicitly construct an extensive set of local integrals of motion for this set of models. Our results can be further generalized to long-range interactions as well as to systems lacking translational invariance.
In lattice models, destructive interference can quench single-particle motion and produce (nearly) dispersionless Bloch bands, known as flat bands. Suppressing kinetic energy enhances the role of interactions and can lead to pairing, constrained dynamics, and localization-like behavior even in translationally invariant settings. This thesis studies attractive Hubbard-type interactions in such flat-band systems using an isolated-band (projected) description, which yields an effective Hamiltonian in a Wannier-orbital basis. The π-flux dice lattice is a convenient focus because its two lowest bands are perfectly flat and degenerate, and their subspace admits compactly localized Wannier functions. This makes the projection straightforward to implement and yields a projected Hamiltonian with a simple, short-range structure. A one-dimensional reference model is used alongside the dice lattice to separate and benchmark the effects of different processes. In Publication I, we construct a class of exact many-body eigenstates of the projected Hamiltonian of generic lattice models with flat bands in which localized unpaired quasiparticles coexist with a background of paired particles in the zero-momentum state. This general result motivates the study of a specific model, the π-flux dice-lattice. Using exact diagonalization and realtime evolution from few-particle initial states, we show that two-body bound states behave ergodically. At the same time, the density and spin distribution retain strong memory of the initial quasiparticle positions at long times. These results demonstrate localization-like dynamics in a translationally invariant flat-band model, where memory arises from projection-induced constraints rather than quenched disorder. In Publication II, we introduce a one-dimensional on-site/bond singlet model whose terms mirror those of the projected dice-lattice Hamiltonian, with tunable couplings controlling their relative strengths. Exact diagonalization shows that, for some couplings, the spectrum and dynamics of the on-site/bond-singlet model closely reproduce those of the projected dice lattice. We then use spectral statistics to probe how the different dynamical regimes manifest in energy-level correlations. In Publication III, we apply spectral statistics to the projected dice lattice using higher-order spacing and gap-ratio diagnostics. We find a robust parity dependence: even particle-number sectors show multi-block GOE behavior within fixed symmetry sectors, while odd particle-number sectors exhibit exact doublets and inter-doublet correlations that are GUE at even orders. The appearance of distinct random-matrix ensembles (GOE and GUE) within the same physical model is an unusual and interesting feature, which calls for a deeper understanding of the hidden symmetry structure of the Hamiltonians obtained by projecting onto the flat-band subspace in the dice lattice and other lattice models with flat bands realized with ultracold gases in optical lattices and in the newly discovered class of moiré materials.
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 demonstrate robust ergodicity breaking in interacting many-body systems in arbitrary Euclidian dimension based on disorder-free many-body localization. Translationally invariant fine-tuned single-particle lattice Hamiltonians can host dispersionless (flat) bands only. Suitable short-range many-body interactions enforce complete suppression of particle transport due to local constraints and lead to ergodicity breaking termed many-body flat-band localization. However, heat might still flow between spatially locked charges. We demonstrate that heat transport is completely suppressed in one dimension. In higher dimensions we establish a universal bound on the filling fraction below which the heat transport is suppressed. The bound is based on the mapping to a classical percolation problem. Above the bound, the heat transport in percolation clusters is additionally affected by emerging bulk disorder and edge scattering induced by local constraints, which work in favor of arresting the heat flow and might keep the ergodicity breaking above the universal bound. We discuss explicit examples in one and two dimensions.
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned coupling. These flat bands display remarkable strongly interacting phases of matter. Originally considered as a theoretical convenience useful for obtaining exact analytical solutions of ferromagnetism, flat bands have now been observed in a variety of settings, ranging from electronic systems to ultracold atomic gases and photonic devices. Here we review the design and implementation of flat bands and chart future directions of this exciting field.
In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme sensitivity to perturbations and interactions. This sensitivity unveils a wide variety of exotic and unconventional physical phenomena. Moreover, the progress in their experimental realization contributes to the expanding landscape of exploration in this field. This thesis aims to summarize all the works throughout the Ph.D. program. Firstly, an in-depth exploration was conducted on the impact of weak quasiperiodic perturbations on one-dimensional two-band all-bands-flat lattices. These tight-binding Hamiltonian are diagonalized through a sequence of local unitary transformations. By adjusting the quasiperiodic potential parameters, the key achievement involves finding a critical-to-insulator transition and identifying fractality edges in the flatband systems with quasiperiodic perturbations. Next, the investigation delved into the effects of on-site interactions among hard-core bosons in one- and two-dimensional cross-stitch lattices. One key finding is that groundstate energy primarily depends on compact localized states. Moreover, the presence of barriers of compact localized states trap bosons, leading to the emergence of non-ergodic excitation and Hilbert space fragmentation. Lastly, a compact localized eigenstate of the one-dimensional diamond chain using an electric circuit was successfully generated via local (linear and non-linear) driving. This achievement opens up a versatile circuit platform for the generation of flatbands and holds promise for potential applications in the field of quantum information. I hope these collective efforts have expanded the frontiers of the field and made a meaningful contribution to the scientific community.