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

¹ Institut für Theoretische Physik, Universität Regensburg, 93053 Regensburg, Germany
² University of Kent, School of Physical Sciences, Canterbury CT2 7NH, UK
³ Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
⁴ Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA
⁵ Institute for Theoretical Physics, Universität Heidelberg, Philosophenweg 12, D-69120 Germany

^* Speaker, e-mail: maksim.ulybyshev@physik.uni-regensburg.de

Published online: 26 March 2018

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.