Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid

Abstract

At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultra-cold atoms, frustrated magnets and quantum Moiré materials, their unbiased presence remain elusive in microscopic two-dimensional lattice models. Here, we show by means of large-scale quantum Monte Carlo simulations of correlated electrons on the $\pi$-flux square lattice subjected to extended Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and an columnar valence bond solid at finite interaction, and a possible Dirac QSL at the infinite yet tractable interaction limit emerge in a coherent sequence. These unexpected novel quantum states resides in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization and the dynamic coupling between emergent matter and gauge fields, will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.

arXiv comment12 pages, 7 figures

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• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet
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• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Emus live on the Gross-Neveu-Yukawa archipelago
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• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Mott insulating states of the anisotropic SU(4) Dirac fermions
• Universal collective Larmor-Silin mode emerging in magnetized correlated Dirac fermions