TY  - JOUR
A1  - Roy, Bitan
A1  - Assaad, Fakher F.
A1  - Herbut, Igor F.
T1  - Zero Modes and Global Antiferromagnetism in Strained Graphene
JF  - Physical Review X
N2  - A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits locally both the Neel and ferromagnetic orders, even for weak Hubbard interaction. Whereas the Neel order parameter remains of the same sign in the entire system, the magnetization at the boundary takes the opposite sign from the bulk. The total magnetization vanishes this way, and the magnetic ground state is globally only an antiferromagnet. This peculiar ordering stems from the nature of the strain-induced single-particle zero-energy states, which have support on one sublattice of the honeycomb lattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical calculation of the order parameters, as well as by the Monte Carlo simulations of the Hubbard model in both uniformly and nonuniformly strained honeycomb lattice. The present result is contrasted with the magnetic ground state of the same Hubbard model in the presence of a true magnetic field (and for vanishing Zeeman coupling), which is exclusively Neel ordered, with zero local magnetization everywhere in the system.
KW  - honeycomb lattice
KW  - dirac fermions
KW  - Hubbard-model
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-116108
SN  - 2160-3308
VL  - 4
IS  - 2
ER  - 
TY  - JOUR
A1  - Assaad, Fakher F.
A1  - Herbut, Igor F.
T1  - Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice
JF  - Physical Review X
N2  - 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 small, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetrybreaking 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 semimetallic and the insulating antiferromagnetic states with increase of the interaction. The single-particle gap, measured in units of 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.
KW  - strongly correlated materials
KW  - mesoscopics
KW  - computational physics
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-129829
VL  - 3
IS  - 031010
ER  -