Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions

Abstract

We investigate the efficacy of shared purity, a measure of quantum correlation that is independent of the separability-entanglement paradigm, as a quantum phase transition indicator in comparison with concurrence, a bipartite entanglement measure. The order parameters are investigated for thermal states and pseudo-thermal states, of the systems considered. In the case of the one-dimensional J1 - J2 Heisenberg quantum spin model and the one-dimensional transverse-field quantum Ising model, shared purity turns out to be as effective as concurrence in indicating quantum phase transitions. In the two-dimensional J1 - J2 Heisenberg quantum spin model, shared purity indicates the two quantum phase transitions present in the model, while concurrence detects only one of them. Moreover, we find diverging finite-size scaling exponents for the order parameters near the transitions in odd- and even-sized systems governed by the one-dimensional J1 - J2 model, as had previously been reported for quantum spins on odd- and even-legged ladders. It is plausible that the divergence is related to a Mo:bius strip-like boundary condition required for odd-sized systems, while for even-sized systems, the usual periodic boundary condition is sufficient.