Information dynamics in a model with Hilbert space fragmentation

Abstract

The fully frustrated ladder – a quasi-1D geometrically frustrated spin one half Heisenberg model – is non-integrable with local conserved quantities on rungs of the ladder, inducing the local fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

“…This phenomenon was referred to as Krylov-Restricted Thermalization in Ref. [19], and evidence for its validity has been found in various fragmented systems [19,120,173,178].…”

“…[172]. Other such examples include certain one-dimensional models with strict confinement [173,126,174], where the Hamiltonian restricted to a Krylov subspace was shown to be the integrable XXZ model, models within the Fibonacci Hilbert space of the Rydberg blockade [175,176], in the presence of frustration [177,178] or dipolar interactions [179]. In addition, several one-dimensional models introduced in earlier literature in various contexts have been shown to exhibit fragmentation, including the Fredkin [180], Motzkin [181], Pair-Flip [117], folded XXZ [20,182,183,184], and Temperley-Lieb spin chains [185,117].…”

“…In strongly fragmented systems, the Krylov-Restricted Thermalization within the nonlocally constrained Krylov subspaces K j can lead to many surprising consequences, including atypical late-time expectation values of local operators [19,178], and an apparent Casimir effect [189]. For example, the infinite-temperature charge density profile within a Krylov subspace of the pair-hopping model of Eq.…”

Information spreading and scrambling in disorder-free multiple-spin interacting models

“…The OTOC is an operator-based quantity to quantify the spread of information and scrambling. The OTOC has been applied to various condensed matter systems, e.g., disordered system [11][12][13][14] and some specific systems [15][16][17][18][19][20][21].…”

Disorder-free localization transition in a two-dimensional lattice gauge theory

“…Several important directions arise from our work. Information spreading in systems with fragmented Hilbert spaces has been studied in 1D [35,36], which naturally poses the question of information spreading in our interacting 2D model [37]. A further key question is the influence of matter fields, which introduce a dynamic charge on top of the static charges in these 2D LGTs thereby inducing a coupling between the previously disconnected superselection sectors of the pure gauge theory.…”