Constructing topological models by symmetrization: A projected entangled pair states study

Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group G˜ which is always non-Abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wave functions in the same phase as the double model of G˜. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of G˜.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Interplay between double-exchange, superexchange, and Lifshitz localization in doped manganites

Considering the disorder caused in manganites by the substitution Mn→Fe or Ga, we accomplish a systematic study of doped manganites begun in previous papers. To this end, a disordered model is formulated and solved using the variational mean-field technique. The subtle interplay between double exchange, superexchange, and disorder causes similar effects on the dependence of T_(C) on the percentage of Mn substitution in the cases considered. Yet, in La_(2/3)Ca_(1/3)Mn_(1-y)Ga_(y)O_(3) our results suggest a quantum critical point (QCP) for y ≈ 0.1–0.2, associated to the localization of the electronic states of the conduction band. In the case of La_(x)Ca_(x)Mn_(1-y)Fe_(y)O_(3) (with x = 1/3,3/8) no such QCP is expected.