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The detection of the (semi)metal-insulator phase transition can be extremelydifficult if the local order parameter which characterizes the ordered phase isunknown.In some cases, it is even impossible to define a local order parameter:the most prominent example of such system is the spin liquid state. This statewas proposed to exist in theHubbard model on the hexagonal lattice in a regionbetween the semimetal phase and the antiferromagnetic insulator phase. Theexistence of this phase has been the subject of a long debate. In order todetect these exotic phases we must use alternative methods to those used formore familiar examples of spontaneous symmetry breaking. We have modified theBackus-Gilbert method of analytic continuation which was previously used in thecalculation of the pion quasiparticle mass in lattice QCD. The modification ofthe method consists of the introduction of the Tikhonov regularization schemewhich was used to treat the ill-conditioned kernel. This modifiedBackus-Gilbert method is applied to the Euclidean propagators in momentum spacecalculated using the hybridMonte Carlo algorithm. In this way, it is possibleto reconstruct the full dispersion relation and to estimate the mass gap, whichis a direct signal of the transition to the insulating state. We demonstratethe utility of this method in our calculations for the Hubbard model on thehexagonal lattice. We also apply the method to the metal-insulator phasetransition in the Hubbard-Coulomb model on the square lattice.

Direct detection of metal-insulator phase transitions using the modified Backus-Gilbert method