Proposal for Realizing Quantum Scars in the Tilted 1D Fermi-Hubbard Model

Abstract

Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg et al., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime U ≈ ∆ ≫ J at electronic filling factor ν = 1. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realisations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the Fermi-Hubbard model is different from other examples in the literature: the scars originate from a subgraph, representing a free spin-1 paramagnet, which is weakly connected to the rest of the Hamiltonian's adjacency graph. Our work demonstrates that correlated fermions in tilted optical lattices provide a platform for understanding the interplay of many-body scarring and other forms of ergodicity breaking, such as localisation and Hilbert space fragmentation.

Many-body Hilbert space scarring on a superconducting processor

“…While breaking the thermalization rendered ergodicity, the QMBS states are distinct from the quantum states in classically integrable systems and from quantum many-body localized states as well [17][18][19][20]. Theoretically, QMBS states have been studied in diverse systems ranging from the Heisenberg spin [21,22], Affleck-Kennedy-Lieb-Tasaki [23,24], extended Hubbard [25][26][27] and Ising [28] models to frustrated [29,30] and topological [31,32] lattices, quantum Hall systems [33,34], Floquet-driven systems [35,36], systems with a flat band [29,37,38], and two-dimensional systems [39]. General theoretical frameworks were developed, in which QMBS states are constructed based on the embedding method [40,41] and quasi-symmetry groups [42].…”

Robustness of Stark many-body localization in the $J_1$-$J_2$ Heisenberg model

“…The resulting features predicted in the localized phase of such models are very much similar to those of MBL systems, which includes includes level spacing ratio (LSR) statistics and memory of initial states [18][19][20][21]. This phenomenon was suggestively called Stark many-body localization (SMBL) [18], and was later predicted to be observed in fermion [21][22][23], spin [24] as well as in topological systems [25]. These theoretical predictions have been recently confirmed by experiential signatures of SMBL in trapped-ions quantum simulators [26].…”

Quantum scars and bulk coherence in a symmetry-protected topological phase

“…In this context, let us note that connections between quantum many-body scars and the proximity to integrable points have already been discussed in Refs. [47,72]. On the other hand, thermalization in integrable models is usually understood with respect to a suitable generalized Gibbs ensemble (GGE), which accounts for the extensive number of conservation laws [5,6].…”

“…The presence of such scar states means that a system will thermalize for most initial conditions, but when initialized in certain specific states (which are often experimentally accessible), atypical dynamics are observed [37]. Subsequent work has substantiated the existence of quantum scars in a variety of models [39][40][41][42][43][44][45][46][47]. In such cases, scars often appear in the form of a "tower of states," i.e., a set of eigenstates with almost equidistant energy spacing forming a nonthermalizing subspace which can be constructed by applying certain raising-type operators [48,49].…”