arXiv:1503.05714 · Physical Review B

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

Clément Février, S. Fratini, Arnaud Ralko

Published Jun 8, 2015• 8 citations

Abstract

The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio ${t}^{\ensuremath{'}}/t$. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

DOI: 10.1103/physrevb.91.245111

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arXiv:1503.05714 · Physical Review B

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

Clément Février, S. Fratini, Arnaud Ralko

Published Jun 8, 2015• 8 citations

arXiv HTML PDF

Abstract

{t}^{\ensuremath{'}}/t

. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell

\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}

droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

DOI: 10.1103/physrevb.91.245111

Related papers

Grenoble Alpes

Jan 1, 20150 citations

Quantum Phase Transition and Local Entanglement in Extended Hubbard Model on Anisotropic Triangular Lattices*

Ji-Ming Gao, Rong-An Tang, Zheng-Mei Zhang +1 more

Abstract Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.Abstract Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.

Communications in Theoretical PhysicsNov 1, 20160 citations

Orbital phases of p -band ultracold fermions in a frustrated triangular lattice

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Physical Review AOct 23, 20243 citations

Orbital phases of $p$ -band ultracold fermions in the frustrated triangular latticeOrbital phases of $p$-band ultracold fermions in the frustrated triangular lattice

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Orbital degrees of freedom play an important role for understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into $p$ -orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Low-temperature phase diagrams are obtained, which contain stripe-, ferro- and para-orbital ordered quantum phases, due to the interplay of anisotropic hoppings and geometrical frustration. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.Orbital degrees of freedom play an important role for understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into $p$-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Low-temperature phase diagrams are obtained, which contain stripe-, ferro- and para-orbital ordered quantum phases, due to the interplay of anisotropic hoppings and geometrical frustration. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.

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Particle-hole asymmetry and pinball liquid in a triangular-lattice extended Hubbard model within the mean-field approximation

Aleksey Alekseev, Agnieszka Cichy, Konrad Jerzy Kapcia

Recently, triangular lattice models have received a lot of attention since they can describe a number of strongly-correlated materials that exhibit superconductivity and various magnetic and charge orders. In this research we present an extensive analysis of the charge-ordering phenomenon of the triangular-lattice extended Hubbard model with repulsive onsite and nearest-neighbor interaction, arbitrary charge concentration, and $\sqrt{3}\times\sqrt{3}$ supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed to identify $8$ charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided a great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for the further research with correlation effects included. Together with atomic-limit approximation it can serve them as both a starting point, and a tool to interpret results.Recently, triangular lattice models have received a lot of attention since they can describe a number of strongly-correlated materials that exhibit superconductivity and various magnetic and charge orders. In this research we present an extensive analysis of the charge-ordering phenomenon of the triangular-lattice extended Hubbard model with repulsive onsite and nearest-neighbor interaction, arbitrary charge concentration, and $\sqrt{3}\times\sqrt{3}$ supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed to identify $8$ charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided a great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for the further research with correlation effects included. Together with atomic-limit approximation it can serve them as both a starting point, and a tool to interpret results.

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Phase stability, charge ordering, and charge-liquid formation in the Falicov–Kimball model on triangular and kagome lattices

Ammar Nejati, Marvin Lenk

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 ( $\mu _f = \mu _c = U/2$ μ f = μ c = U / 2 ), “generalized” half-filling ( $\bar{n}_f = 1/3$ n ¯ f = 1 / 3 , $\bar{n}_c = 2/3$ n ¯ c = 2 / 3 ), and conventional half-filling ( $\bar{n}_f = \bar{n}_c = 1/2$ n ¯ f = n ¯ 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. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.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 ( $$\mu _f = \mu _c = U/2$$ μ f = μ c = U / 2 ), “generalized” half-filling ( $$\bar{n}_f = 1/3$$ n ¯ f = 1 / 3 , $$\bar{n}_c = 2/3$$ n ¯ c = 2 / 3 ), and conventional half-filling ( $$\bar{n}_f = \bar{n}_c = 1/2$$ n ¯ f = n ¯ 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. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.

arXiv:2608.28898The European Physical Journal BSep 1, 20260 citations

{t}^{\ensuremath{'}}/t

. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell

\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}

p

-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Due to the interplay of anisotropic hoppings and geometrical frustration, a rich phase diagram is found, including stripe-orbital, paraorbital, and ferro-orbital phases, in contrast to its bosonic analog with orbital-skyrmion ordering in the identical lattice. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.

Orbital phases of

p

-band ultracold fermions in the frustrated triangular lattice

p

-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Low-temperature phase diagrams are obtained, which contain stripe-, ferro- and para-orbital ordered quantum phases, due to the interplay of anisotropic hoppings and geometrical frustration. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.

\sqrt{3}\times\sqrt{3}

supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed to identify

8

charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided a great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for the further research with correlation effects included. Together with atomic-limit approximation it can serve them as both a starting point, and a tool to interpret results.

\mu _f = \mu _c = U/2

μ f = μ c = U / 2 ), “generalized” half-filling (

\bar{n}_f = 1/3

n ¯ f = 1 / 3 ,

\bar{n}_c = 2/3

n ¯ c = 2 / 3 ), and conventional half-filling (

\bar{n}_f = \bar{n}_c = 1/2

n ¯ f = n ¯ 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. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.