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(Abridged) We present a systematic investigation of physical conditions andelemental abundances in four optically thick Lyman-limit systems (LLSs) at$z=0.36-0.6$ discovered within the Cosmic Ultraviolet Baryon Survey (CUBS).CUBS LLSs exhibit multi-component kinematic structure and a complex mix ofmultiphase gas, with associated metal transitions from multiple ionizationstates that span several hundred km/s in line-of-sight velocity. Specifically,higher column density components (log N(HI)>16) in all four absorbers comprisedynamically cool gas with $\langle T \rangle =(2\pm1) \times10^4\,$K and modestnon-thermal broadening of $5\pm3\,$ km/s. The high quality of the QSOabsorption spectra allows us to infer the physical conditions of the gas, usinga detailed ionization modeling that takes into account the resolved componentstructures of HI and metal transitions. The range of inferred gas densitiesindicates that these absorbers consist of spatially compact clouds with amedian line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robustmetallicity constraints for the low-density, highly ionized phase remainschallenging due to the uncertain N(HI), we demonstrate that the cool-phase gasin LLSs has a median metallicity of$\mathrm{[\alpha/H]_{1/2}}=-0.7^{+0.1}_{-0.2}$, with a 16-84 percentile rangeof $\mathrm{[\alpha/H]}=(-1.3,-0.1)$. Furthermore, the wide range of inferredelemental abundance ratios ($\mathrm{[C/\alpha]}$, $\mathrm{[N/\alpha]}$, and$\mathrm{[Fe/\alpha]}$) indicate a diversity of chemical enrichment histories.Combining the absorption data with deep galaxy survey data characterizing thegalaxy environment of these absorbers, we discuss the physical connectionbetween star-forming regions in galaxies and diffuse gas associated withoptically thick absorption systems in the $z<1$ circumgalactic medium.

The Cosmic Ultraviolet Baryon Survey (CUBS) -- III. Physical properties and elemental abundances of Lyman limit systems at $z<1$