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At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. While such states are possibly realized in two-dimensional organic compounds, they have remained elusive in experimentally relevant microscopic two-dimensional models. Here, we show by means of large-scale quantum Monte Carlo simulations of correlated fermions on the honeycomb lattice, a structure realized in graphene, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Therefore, the possibility of unconventional superconductivity through doping arises. We foresee its realization with ultra-cold atoms or with honeycomb lattices made with group IV elements.
We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully
We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent g
Relativistic massless Dirac fermions can be probed with high-energy physics experiments, but appear also as low-energy quasi-particle excitations in electronic band structures. In condensed matter systems, their massless nature can be protected by cr
An unbiased zero-temperature auxiliary-field quantum Monte Carlo method is employed to analyze the nature of the semimetallic phase of the two-dimensional Hubbard model on the honeycomb lattice at half filling. It is shown that the quasiparticle weig
Two-dimensional Dirac fermions are subjected to two types of interactions, namely the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $alpha$ is larger than some critical va