Contributor info: Dr Paul A. McClarty

Dominik Hahn, Paul A. McClarty, David J. Luitz

SciPost Phys. 11, 074 (2021) · published 6 October 2021 | Toggle abstract · pdf

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 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 and whose persistence is therefore a consequence of fragmentation. 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.

Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz

SciPost Phys. 7, 064 (2019) · published 21 November 2019 | Toggle abstract · pdf

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.