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 twopoint 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 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.

Nature of the phases in the frustratedXYmodel on the honeycomb lattice

“…Another model that has recently received considerable attention for its potential to realize spin-liquid states is the spin-1/2 Heisenberg model on the honeycomb lattice, with nearest-neighbor (NN) J 1 and next-to-nearest neighbor (NNN) J 2 exchange interactions [7][8][9][10][11][12][13][14][15][16]. This is in part motivated by its close relation to the Hubbard model, for which the possibility of having a spin-liquid ground state has been under close scrutiny [17][18][19].A closely related spin model with a rich phase diagram and the promise to support a gapless spin liquid phase is the J 1 − J 2 spin-1/2 XY model on the honeycomb lattice [20,21], which is the main subject of this Rapid Communication. Its Hamiltonian can be written as…”

Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

“…This makes the task of detecting order especially challenging. An alternative way to calculate order parameters is to apply a small pinning field in the Hamiltonian, and detect the order induced by the pinning field 27,28 . For pairing we could now applŷ…”

Triplet p + ip pairing correlations in the doped Kane-Mele-Hubbard model: A quantum Monte Carlo study

“…Recently, a new research field has emerged in condensed matter physics which is based on the findings that a spin-orbit interaction can lead to topological electronic phase transitions [1] and the electron-electron interactions can produce these transitions [2][3][4][5][6][7][8][9]. This new field makes it natural to ask what remarkable new properties and transitions might occur between distinct, competing correlated topological electron phases when the spin-orbit interaction is present.…”

“…Numerical simulations point to other novel states of matter tied to the strength of the electron-electron interaction and spin-orbit coupling. In particular, if U is the strength of the local Coulomb interaction and t the hopping amplitude to nearest neighbor sites, the Hubbard model on a honeycomb lattice is known to have a semimetal phase at small U and an antiferromagnetic one at large U [19], and ground-state quantum Monte Carlo (QMC) simulations performed at half-filling suggest a transition from a semimetal to an insulating antiferromagnetic state insulator when U/t≈3.5 [8,19]. On the other hand, other quantum Monte Carlo studies, such as the finite temperature determinant quantum Monte Carlo method [10], find that strong antiferromagnetic fluctuations dominate around half filling and strong ferromagnetic correlations dominate at less than 3/4-filling.…”

“…This new field makes it natural to ask what remarkable new properties and transitions might occur between distinct, competing correlated topological electron phases when the spin-orbit interaction is present. Various researchers have proposed [4][5][6][7][8][9] the Hubbard model with spinorbit interactions (the Kane-Mele-Hubbard model) on a honeycomb-like lattice, as a starting point for answering these questions.…”