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

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.

ENTANGLEMENT ENTROPY AND STRONGLY CORRELATED TOPOLOGICAL MATTER

Topological ordered phases are gapped states of matter that are characterized by non-local entanglement in their ground state wave functions instead of a local order parameter. In this paper, we review some of the basic results on the entanglement structure of topologically ordered phases. In particular, we focus on the notion and uses of "topological entanglement entropy" in two and higher dimensions, and also briefly review the relation between entanglement spectrum and the spectrum of the physical edge states for chiral topological states. Furthermore, we discuss a curvature expansion for the entanglement entropy which sharpens the nonlocality of topological entanglement entropy.

Picosecond Pulsed Laser Induced Melting of Monocrystalline Copper: A Hybrid Simulation

A hybrid method combing molecular dynamics and two-step radiation heating model is used to study the kinetics and microscopic mechanisms of picosecond laser melting of monocrystalline copper in stress confinement regime. The nonequilibrium processes of laser melting are simulated by classical MD method, and laser excitation as well as subsequent relaxation of the conduction band electrons are described continually by two-step radiation heating model. The mechanism responsible for melting of copper under picosecond laser pulse irradiation can be attributed to homogeneous nucleation of the liquid phase inside the solid region. The speed of stress wave is predicted to be 4400m/s equal to that of sound. The liquid and crystal regions are identified definitely in the atomic configurations by means of Local Order Parameter, in-plane structure and number density of atoms. Velocity-reducing technique is proved efficient in avoiding the influence of the reflected stress wave on melting process by comparing two models with velocity-reducing technique and free boundary condition at the bottom respectively.