Quantum Many-body Scars in a Landau Level on a Thin Torus

Abstract

We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling ν = 1/3, the model exactly maps onto the so-called "PXP model", a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors ν = p/(2p + 1), and show that the model is equivalent to non-integrable spinchains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems

“…These higher-moment conserving models have attracted much attention in the context of fractons [11][12][13][14][15][16][17], and are realizable in synthetic quantum matter [18] or solid state systems [19]. In particular, the intertwined relation between the internal charge conservation law and its dipole moment has recently been shown to have significant impact on nonequilibrium properties [20][21][22][23][24][25][26][27]. In the most severe cases, for short-ranged interactions and low spin representations, the system fails to thermalize due to a strong fragmentation of the many-body Hilbert space into exponentially many disconnected sectors [21,22], giving rise to statistically localized integrals of motion [27].…”

“…., a model that has been studied in the context of Hilbert space fragmentation [21][22][23][24][25][26][27].…”

Kinetically constrained freezing transition in a dipole-conserving system

“…While MBL systems rely on the quenched breaking of translational invariance to induce localization, the search for mechanisms to circumvent thermalization in translationally-invariant systems is also an active area of research [27][28][29][30][31][32][33][34][35]. Among recent developments in this direction is the exploration of constrained quantum systems such as Rydberg-blockaded chains [36], which has lead to a surge of research on nonthermal "quantum scar" states [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51], and models with fracton-like excitations [52][53][54][55][56], which have been shown to exhibit a form of localization under certain ideal conditions [57][58][59][60][61]. In this work we explore a dynamical phase transition between thermalizing and frozen phases that occurs in one such system with fracton-like constraints on the dynamics.…”

Weak-ergodicity-breaking via lattice supersymmetry

“…These states, recently dubbed quantum many-body scars [10], have been linked to anomalously slow dynamics observed in laser-dressed Rydberg atom ensembles [11], and have attracted a considerable theoretical effort [10,[12][13][14][15][16][17][18][19][20]. While a number of models supporting quantum manybody scars have recently been found [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the general conditions (if any) for stabilizing ETH-violating states are still unknown, and the role of symmetries in this context stands as an open question.…”