Calculating the spectrum of the charmed baryons from Lattice QCD

We extract the spectrum of charmed baryons on $32^3 \times 64$, $2+1$-flavor gauge ensembles. Calculations are performed with almost physical light quarks, $m_\pi \sim 156$ MeV, and physical strange and charm quarks. A relativistic heavy-quark action is used for valance charm quarks to suppress the systematic errors. We employ a two-fold variational analysis in order to access the excited states by varying the interpolating operators and smearing parameters independently. In this talk, we report on the details and status of our calculations and present the results for positive and negative parity, spin-$1/2$ and spin-$3/2$ states.