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.
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.
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.
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.
Abstract We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.
We find that a flat-band fermion system with interactions and without disorders exhibits nonthermalized ergodicity-breaking dynamics, an analog of many-body localization (MBL). In the previous works we observed flat-band many-body localization (FMBL) in the Creutz ladder model. The origin of FMBL is a compact localized state governed by local integrals of motion (LIOMs), which are to be obtained explicitly. In this work we clarify the dynamical aspects of FMBL. We first study dynamics of two particles, and find that the states are not substantially modified by weak interactions, but the periodic time evolution of entanglement entropy emerges as a result of a specific mechanism inherent in the system. On the other hand, as the strength of the interactions is increased, the modification of the states takes place with inducing instability of the LIOMs. Furthermore, many-body dynamics of the system at finite fillings is numerically investigated by the time-evolving block decimation (TEBD) method. For a suitable choice of the filling, nonthermal and low entangled dynamics appears. This behavior is a typical example of the disorder-free FMBL.
We explore the problem of localization in topological and nontopological nearly-flat subbands derived from the lowest Landau level, in the presence of quenched disorder and short-range interactions. We consider two models: a suitably engineered periodic potential and randomly distributed pointlike impurities. We perform numerical exact diagonalization on a torus geometry and use the mean level spacing ratio $\ensuremath{\langle}r\ensuremath{\rangle}$ as a diagnostic of ergodicity. For topological subbands, we find there is no ergodicity breaking in both the one- and two-dimensional thermodynamic limits. For nontopological subbands, in contrast, we find evidence of an ergodicity breaking transition at finite disorder strength in the one-dimensional thermodynamic limit. Intriguingly, indications of similar behavior in the two-dimensional thermodynamic limit are found as well. This constitutes a novel, continuum setting for the study of the many-body localization transition in one and two dimensions.
We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By studying eigenstates of the full Hamiltonian, for strong disorders we find that the dynamics is confined up to very long times to disconnected MB clusters in the Fock space. By keeping only resonant contributions and simplifying the quantum problem to rate equations (REs) for MB states, in analogy with percolation problems, the MBL transition is located via the universal cluster distribution and the emergence of the macroscopic cluster. On the ergodic side, our approximate RE approach to the relaxation processes captures well the diffusion transport, as found for the full quantum model. In a broad transient regime, we find an anomalous, i.e., subdiffusivelike, transport, emerging from weak links between MB states.