Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice

Abstract

In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is {\it small}, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry breaking field, and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary field quantum Monte Carlo algorithm. With our enhanced resolution we find a direct and continuous quantum phase transition between the semi-metallic and the insulating antiferromagnetic states with increase of the interaction. The single particle gap in units of the Hubbard $U$ tracks the staggered magnetization. An excellent data collapse is obtained by finite size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.

7 pages, 6 figures, Published version

References in corpus (6)

• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model

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