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.
Highlights
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
How can we characterize the asymptotic, or long time, behavior of the model? To what extent does this depend on the initial state? What are the asymptotic states within dynamically disconnected fragments and how do these collectively lead to violations of eigenstate thermalization hypothesis (ETH)? Can we understand the dynamics of operator spreading in terms of the fragmentation picture? What is the effect of weakly lifting the frustration thereby breaking the local conservation laws? In this paper, we systematically investigate features of the dynamics in one model with a fragmented Hilbert space: the fully frustrated ladder [43, 52,53,54]
The central observation of this work is that large enough fragments thermalize in the sense of obeying the eigenstate thermalization hypothesis but the Hilbert space is exponentially dominated by short chain fragments that are far from thermal
Summary
The study of non-equilibrium quantum dynamics is one of the main frontiers of contemporary physics. While much remains to be explored and understood there are a few central results that help to frame questions of current interest One of these is the observation that observables tend to thermalize at long times in local quantum many-body systems in the sense that the Gibbs ensemble of statistical mechanics becomes a good description of the asymptotic properties of the system even when the initial state is a single eigenstate. We show that we get an excellent correspondence between the observed long-time properties and the entropy computed from states that are randomized within each conserved sector This means that the system thermalizes as much as it can in the conventional sense of ETH but the small fragments overwhelm the gross behavior of the system so that it is highly athermal overall. While the model is interesting on its own, we discuss in the conclusions some features of the dynamics that are expected to occur in all models with Hilbert space fragmentation
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