Phase stability, charge ordering, and charge-liquid formation in the Falicov-Kimball model on triangular and kagome lattices
Abstract
We present a systematic investigation of the stability of the phase diagram of the spinless Falicov-Kimball model on two-dimensional non-bipartite lattices, the triangular and kagome lattices, using Markov-chain Monte Carlo simulations. Three filling or chemical potential conditions are examined: fixed chemical potentials (μf = μc = U/2), "generalized" half-filling (n̅f = 1/3, n̅c = 2/3), and conventional half-filling (n̅f = n̅c = 1/2). For each condition, the effects of a perturbatively small next-nearest-neighbor hopping are studied. On the triangular lattice, Anderson insulator, Mott insulator, and charge-density wave (CDW) phases are found in all cases, with the CDW driven by Coulomb-interaction-mediated nesting. Evidence for a charge-liquid regime is found in the region between the weakly correlated regime and the CDW, characterized by competing charge-ordering wavevectors and the absence of universal scaling behavior, whose extent shrinks progressively from the grand-canonical to the conventional half-filling condition. On the kagome lattice, the CDW phase is completely absent; instead, an insulating ground state, plausibly of the Mott type, is found, with signatures of a possible quantum phase transition at zero temperature. Our results establish the crucial role of lattice geometry and particle-hole symmetry breaking in shaping the phase diagram of correlated electron systems.
Versions
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BibTeX
@misc{nejati2026phase,
title = {{Phase stability, charge ordering, and charge-liquid formation in the Falicov-Kimball model on triangular and kagome lattices}},
author = {Ammar Nejati and Marvin Lenk},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28898},
eprint = {2608.28898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28898},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phase stability, charge ordering, and charge-liquid formation in the Falicov-Kimball model on triangular and kagome lattices
AU - Ammar Nejati
AU - Marvin Lenk
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28898
UR - https://arxiv.org/abs/2608.28898
AB - We present a systematic investigation of the stability of the phase diagram of the spinless Falicov-Kimball model on two-dimensional non-bipartite lattices, the triangular and kagome lattices, using Markov-chain Monte Carlo simulations. Three filling or chemical potential conditions are examined: fixed chemical potentials (μ_f = μ_c = U/2), "generalized" half-filling (n̅_f = 1/3, n̅_c = 2/3), and conventional half-filling (n̅_f = n̅_c = 1/2). For each condition, the effects of a perturbatively small next-nearest-neighbor hopping are studied. On the triangular lattice, Anderson insulator, Mott insulator, and charge-density wave (CDW) phases are found in all cases, with the CDW driven by Coulomb-interaction-mediated nesting. Evidence for a charge-liquid regime is found in the region between the weakly correlated regime and the CDW, characterized by competing charge-ordering wavevectors and the absence of universal scaling behavior, whose extent shrinks progressively from the grand-canonical to the conventional half-filling condition. On the kagome lattice, the CDW phase is completely absent; instead, an insulating ground state, plausibly of the Mott type, is found, with signatures of a possible quantum phase transition at zero temperature. Our results establish the crucial role of lattice geometry and particle-hole symmetry breaking in shaping the phase diagram of correlated electron systems.
ER -