We investigate the implications of integrability for the existence of quantumdisentangled liquid (QDL) states in the half-filled one-dimensional Hubbardmodel. We argue that there exist finite energy-density eigenstates that exhibitQDL behaviour in the sense of J. Stat. Mech. P10010 (2014). These states areatypical in the sense that their entropy density is smaller than that ofthermal states at the same energy density. Furthermore, we show that thermalstates in a particular temperature window exhibit a weaker form of the QDLproperty, in agreement with recent results obtained by strong-couplingexpansion methods in arXiv:1611.02075. This article is part of the themed issue`Breakdown of ergodicity in quantum systems: from solids to synthetics matter'.
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