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.

15 pages with 7 figures and 9 tables including supplementary information, accepted for publication in Scientific Reports

References in corpus (4)

• The electronic properties of graphene
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets

Cited by in corpus (28)

• Dirac materials
• Correlation effects in two-dimensional topological insulators
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Phase diagram of the Kane-Mele-Coulomb model
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• Instabilities on graphene's honeycomb lattice with electron-phonon interactions
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Chiral spin density wave order on frustrated honeycomb and bilayer triangle lattice Hubbard model at half-filling
• Impurity-induced magnetic moments on the graphene-lattice Hubbard model: an inhomogeneous cluster DMFT study
• Disappearance of the Dirac cone in silicene due to the presence of an electric field
• A stable Algebraic Spin Liquid in a Hubbard model
• Quantum phases of hard-core bosons in a frustrated honeycomb lattice
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Quantum paramagnet in a $\pi$ flux triangular lattice Hubbard model
• Sign Structure, Electron Fractionalization, and Emergent Gauge Description of the Hubbard Model
• Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Universality Class of the Mott Transition
• Coexistence of antiferromagnetism and superconductivity of t-t${}^{\prime }$-J model on honeycomb lattice
• Metal-Insulator Transition of Dirac Fermions: Variational Cluster Study
• Spontaneous loop-spin current with topological characters in the Hubbard model
• Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator
• Exact ground state for the four-electron problem in a 2D finite honeycomb lattice