Abstract
The detection of the (semi)metal-insulator phase transition can be extremely difficult if the local order parameter which characterizes the ordered phase is unknown. 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 state was proposed to exist in the Hubbard model on the hexagonal lattice in a region between the semimetal phase and the antiferromagnetic insulator phase. The existence of this phase has been the subject of a long debate. In order to detect these exotic phases we must use alternative methods to those used for more familiar examples of spontaneous symmetry breaking. We have modified the Backus-Gilbert method of analytic continuation which was previously used in the calculation of the pion quasiparticle mass in lattice QCD. The modification of the method consists of the introduction of the Tikhonov regularization scheme which was used to treat the ill-conditioned kernel. This modified Backus-Gilbert method is applied to the Euclidean propagators in momentum space calculated using the hybrid Monte Carlo algorithm. In this way, it is possible to reconstruct the full dispersion relation and to estimate the mass gap, which is a direct signal of the transition to the insulating state. We demonstrate the utility of this method in our calculations for the Hubbard model on the hexagonal lattice. We also apply the method to the metal-insulator phase transition in the Hubbard-Coulomb model on the square lattice.
Highlights
Methods commonly used in lattice QCD have been applied with great success to certain strongly-correlated electronic systems [1, 2]
We do not find evidence in favor of the spin-liquid phase for the Hubbard model on the hexagonal lattice and we find that our new method for analytic continuation (AC) allows one to accurately determine the location and nature of the Mott-Hubbard transition
We find that for a desired resolution in frequency space, Tikhonov regularization yields the spectral function with the smallest error
Summary
Methods commonly used in lattice QCD have been applied with great success to certain strongly-correlated electronic systems [1, 2]. A second direction has been to directly simulate the manybody lattice Hamiltonian using path integral quantization and applying the highly successful hybrid Monte Carlo approach to the theory [8,9,10] Both of these approaches to strongly-correlated electronic systems have attempted to characterize their phase structure in a controlled, non-perturbative manner. In certain cases, such as the semimetalinsulator transition in the graphene EFT, or more precisely, the transition from the semimetal to the charge density wave (CDW) phase, the order parameter is known (the chiral condensate, ⟨ψψ⟩). In order to do so, one must resort to looking at other, inherently non-local quantities, most notably spectral functions
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