Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice

Abstract

A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.

Artificial honeycomb lattices for electrons, atoms and photons

“…[82] have been recently addressed in Ref. [83], by QMC simulations of the same model in larger clusters (containing up to 2592 sites), finding very weak evidence of a spin liquid phase.…”

Chirald-wave superconductivity in doped graphene

“…For example, magnetism has experimentally been reported both in nanographene [58,59,60], and in graphite in the presence of disorder [61] or grain boundaries [62], although pristine graphene has not been found to be either magnetic [63] or gapped [64,20]. Theoretically, on-site Coulomb repulsion exceeding U > 3.9t has been found to give an antiferromagnetic state in undoped graphene in quantum Monte Carlo simulations [15,17]. This relatively large value of U is a consequence of undoped graphene being a semimetal with only a point-like Fermi surface.…”

“…[4,5,6,7,8,9,10,11,12,13,14,15,17,16]). There, the predominant ordering tendencies are in the particle-hole channel, and usually superconductivity is not among the leading candidates.…”

“…A large number of exotic states of matter has been proposed theoretically, see e.g. [4,5,6,7,8,9,10,11,12,13,14,15,16,17], but most have not been experimentally observed as of yet. One exception is multi-layer graphene systems where there are now experimental reports of an energy gap opening at low temperatures, which has been ascribed to interactions effects [18,19,20,21,22,23,24,25].…”

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…”