Superconformal Cardy states and entanglement structure of 1D quantum critical points with emergent supersymmetry

Condensed matter systems with quantum critical points exhibiting emergent spacetime supersymmetry in the long-wavelength, low-energy limit have attracted much attention recently. In particular, several elements of the N=1 series of superconformal minimal models originally discovered by Friedan, Qiu, and Shenker in 1985 have been realized recently in a variety of 1D quantum lattice models ranging from anyonic spin chains to interacting Majorana chains and boson-fermion mixtures. To better understand the entanglement structure of these exotic quantum critical points, we revisit the problem of the construction of boundary states for the superconformal minimal models and find a new set of Cardy states not previously discussed. As an application of this formalism we present and discuss numerical DMRG results for the entanglement spectrum of the Grover--Sheng--Vishwanath model as a lattice realization of the tricritical Ising universality class.