Hybrid Monte-Carlo simulation of interacting tight-binding model of graphene

Abstract

In this work, results are presented of Hybrid-Monte-Carlo simulations of the tight-binding Hamiltonian of graphene, coupled to an instantaneous long-range two-body potential which is modeled by a Hubbard-Stratonovich auxiliary field. We present an investigation of the spontaneous breaking of the sublattice symmetry, which corresponds to a phase transition from a conducting to an insulating phase and which occurs when the effective fine-structure constant $\alpha$ of the system crosses above a certain threshold ${\alpha }_C$. Qualitative comparisons to earlier works on the subject (which used larger system sizes and higher statistics) are made and it is established that ${\alpha }_C$ is of a plausible magnitude in our simulations. Also, we discuss differences between simulations using compact and non-compact variants of the Hubbard field and present a quantitative comparison of distinct discretization schemes of the Euclidean time-like dimension in the Fermion operator.

7 pages, 1 figure, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

References in corpus (7)

• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Is graphene in vacuum an insulator?
• Lattice field theory simulations of graphene
• How close can one approach the Dirac point in graphene experimentally?
• Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
• Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
• Lifshitz and Excited State Quantum Phase Transitions in Microwave Dirac Billiards

Cited by in corpus (3)

• A density of states approach to the hexagonal Hubbard model at finite density
• Schur complement solver for Quantum Monte-Carlo simulations of strongly interacting fermions
• On the semimetal-insulator transition and Lifshitz transition in simulations of mono-layer graphene