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arXiv:2504.13086 · Physical Review Letters

Many-Body Cages: Disorder-Free Glassiness from Flat Bands in Fock Space and Many-Body Rabi Oscillations

Tom Ben-Ami, Markus Heyl, Roderich Moessner

Published Jul 30, 2026• 3 citations
arXivHTMLPDF

Abstract

We introduce many-body caging as a novel mechanism for nonthermal behavior in quantum matter. We define many-body cages as eigenstates that, through quantum interference, become localized on a subgraph of the many-body state graph. These many-body cages can lead to the formation of flat bands in the many-body spectrum at characteristic, system-independent energies. These flat bands can realize a novel type of glassy eigenspectrum order in the absence of disorder, which we quantify by a band-overlap order parameter with an intricate, possibly fractal, distribution over the many-body state graph. We further show that these many-body cages exhibit distinctive signatures in experimentally accessible quantities, such as through a nonvanishing long-time memory of the initial condition, and many-body Rabi oscillations set by the characteristic flat-band energies. While our predictions in principle apply to any constrained quantum system, we demonstrate them here for 2D lattice gauge theories and models relevant for current experiments in Rydberg atoms. We expect that these many-body cages offer a promising route to realize nonequilibrium quantum states with novel properties.

DOI
10.1103/gmw6-x94c

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We introduce many-body caging as a novel mechanism for nonthermal behavior in quantum matter. We define many-body cages as eigenstates that, through quantum interference, become localized on a subgraph of the many-body state graph. These many-body cages can lead to the formation of flat bands in the many-body spectrum at characteristic, system-independent energies. These flat bands can realize a novel type of glassy eigenspectrum order in the absence of disorder, which we quantify by a band-overlap order parameter with an intricate, possibly fractal, distribution over the many-body state graph. We further show that these many-body cages exhibit distinctive signatures in experimentally accessible quantities, such as through a nonvanishing long-time memory of the initial condition, and many-body Rabi oscillations set by the characteristic flat-band energies. While our predictions in principle apply to any constrained quantum system, we demonstrate them here for 2D lattice gauge theories and models relevant for current experiments in Rydberg atoms. We expect that these many-body cages offer a promising route to realize nonequilibrium quantum states with novel properties.
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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.
Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.
The ongoing quest for understanding nonequilibrium dynamics of complex quantum systems underpins the foundation of statistical physics as well as the development of quantum technology. Quantum many-body scarring has recently opened a window into novel mechanisms for delaying the onset of thermalization by preparing the system in special initial states, such as the Z2{\mathbb{Z}}_{2}Z2​ state in a Rydberg atom system. Here we realize many-body scarring in a Bose-Hubbard quantum simulator from previously unknown initial conditions such as the unit-filling state. We develop a quantum-interference protocol for measuring the entanglement entropy and demonstrate that scarring traps the many-body system in a low-entropy subspace. Our work makes the resource of scarring accessible to a broad class of ultracold-atom experiments, and it allows one to explore the relation of scarring to constrained dynamics in lattice gauge theories, Hilbert space fragmentation, and disorder-free localization.
Quantum many-body scars in Rydberg atom arrays have thus far only been observed on bipartite lattices, leaving open the question of whether and how they survive frustration, and what the appropriate initial states are that lead to nonthermal dynamics. We introduce a graph-theoretic framework to find suitable candidates for scarring on arbitrary lattices. Our framework predicts two distinct mechanisms: type-I scars generalize the bipartite case by using locally entangled states to overcome mild frustration, while type-II scars exploit strong frustration to pin part of the lattice, leaving the remainder to oscillate freely. We numerically demonstrate both mechanisms and uncover an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization. Our results establish scarring as a generic feature of Rydberg systems beyond one dimension and provide an experimentally accessible route to systematically probing non-thermal dynamics in quantum simulators.
We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [C. Danieli et al., Phys. Rev. B 104, 085131 (2021)], we identified the subset of these networks that shows nonlinear caging in the presence of Kerr-like local nonlinearities, i.e., it preserves nonexcited network sites and therefore keeps compact excitations compact. Here we replace nonlinear terms by Bose-Hubbard interactions and study quantum caging. We identify the quantum caging conditions that are related to the nonlinear caging conditions and that guarantee the existence of an extensive set of conserved quantities in any lattice dimension, as first revealed in Tovmasyan et al. [Phys. Rev. B 98, 134513 (2018)] for a set of specific networks. Consequently, transport is realized through moving pairs of interacting particles that break the single-particle caging. We further prove the existence of degenerate energy renormalized compact states for any finite number MMM of participating particles in one- and higher-dimensional lattice---results that explain and generalize previous observations for two particles on a diamond chain [Vidal et al., Phys. Rev. Lett. 85, 3906 (2000)].