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We explore the possibility of a Berezinskii-Kosterlitz-Thouless-like criticalphase for the charge degrees of freedom in the intermediate-temperature regimebetween the charge-ordered and disordered phases in two-dimensional systemswith competing short-range Coulomb repulsion. As the simplest example, weinvestigate the extended Hubbard model with on-site and nearest-neighborCoulomb interactions on a triangular lattice at half filling in the atomiclimit by using a classical Monte Carlo method, and find a critical phase,characterized by algebraic decay of the charge correlation function, belongingto the universality class of the two-dimensional XY model with a $\mathbb{Z}_6$anisotropy. Based on the results, we discuss possible conditions for thecritical phase in materials.

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion