Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0811.1575

Quantum Phase Transitions in the Hubbard Model on Triangular Lattice

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

Published Nov 10, 2008• 1 citation
arXivHTMLPDF

Abstract

We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group (PIRG) method with a new iteration scheme proposed recently. It is found that as the Hubbard interaction $U$ increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at $U_{c1}\sim 7.7t$, which is followed by another first-order transition to a $120^\circ$ Néel ordered state at $U_{c2}\sim 10t$, where $t$ is the transfer integral. Our results ensure the existence of the intermediate NMI phase, and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions. We find that $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ is located in the NMI phase close to the metal-insulator transition point.

DOI
10.48550/arxiv.0811.1575

Related papers

Quantum Phase Transitions in the Hubbard Model on a Triangular Lattice

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group method with a new iteration and truncation scheme proposed recently. It is found for a cluster of 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1 approximately 7.4t, which is followed by another first-order transition to a 120 degrees Néel ordered state at Uc2 approximately 9.2t, where t is the transfer integral. The size dependence of the results is also addressed. Our results suggest the existence of the intermediate NMI phase and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions.

Physical Review Letters•Jul 16, 2009•144 citations

Mott transition in the Hubbard model on the triangular lattice

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at $U_{\rm c} \sim 7.4t$ , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.

physica status solidi (b)•Feb 17, 2010•2 citations

Mott Transition in the Hubbard Model on Checkerboard Lattice

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

We investigate the bandwidth-controlled Mott transition in the Hubbard model on the checkerboard lattice at half filling using the path-integral renormalization group (PIRG) method. It is demonstrated that the system undergoes a first-order phase transition to the plaquette-singlet insulating phase at a finite Hubbard interaction. This conclusion is drawn via a detailed analysis of the spin and charge correlations around the phase transition point by means of the PIRG method aided with a new iteration scheme introduced in this paper.

arXiv:0808.1116•Journal of the Physical Society of Japan•Sep 25, 2008•18 citations

Mott metal-insulator transition in the half-filled Hubbard model on the triangular lattice

Massimo Capone, Luca Capriotti, Federico Becca +1 more

We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.

arXiv:cond-mat/0006437•Physical review. B, Condensed matter•Feb 2, 2001•51 citations

Ground-state phase diagram of the triangular lattice Hubbard model by the density-matrix renormalization group method

Tomonori Shirakawa, Takami Tohyama, J. Kokalj +2 more

Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction $U$ at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ ($t$ being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For $U>{U}_{\mathrm{c}2}$, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For ${U}_{\mathrm{c}1}<U<{U}_{\mathrm{c}2}$, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the $\mathrm{K}$ and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing $U$ and thus the superconductivity is unlikely in the intermediate phase.

arXiv:1606.06814•Physical review. B./Physical review. B•Nov 15, 2017•88 citations

On the Magnetic and Metal-Insulator Transitions in a Two-Dimensional Hubbard Model

Hisashi Kondo, Tôru Moriya

Antiferromagnetic and metal to insulator transitions in the ground state of two-dimensional half-filled and nearly half-filled Hubbard models with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Green's function approach with the self-energy up to the second order in the coupling constant U . For a choice of the parameter value t ′ / t =0.2 the half-filled model undergoes the first order phase transition between paramagnetic metallic (PM) phase and antiferromagnetic insulator (AFI) phase at U / t =4.0 while the first order transition between PM and antiferromagnetic metallic (AFM) phases takes place for nearly half-filled band. The one-electron spectral density is calculated for the PM, AFM, and AFI phases near the phase boundaries. In the PM phase the quasi-particle dispersion indicates the band narrowing from the Hartree-Fock results and the flat band behavior as was indicated by previous stadies and was observed in high- T c cuprates. The quasi-particle dispersion in the AFM phase is seen to be close to the Hartree-Fock results.

Journal of the Physical Society of Japan•Jan 15, 1998•4 citations
We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group (PIRG) method with a new iteration scheme proposed recently. It is found that as the Hubbard interaction UUU increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1∼7.7tU_{c1}\sim 7.7tUc1​∼7.7t, which is followed by another first-order transition to a 120∘120^\circ120∘ Néel ordered state at Uc2∼10tU_{c2}\sim 10tUc2​∼10t, where ttt is the transfer integral. Our results ensure the existence of the intermediate NMI phase, and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions. We find that κκκ-(BEDT-TTF)2_22​Cu2_22​(CN)3_33​ is located in the NMI phase close to the metal-insulator transition point.
We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group method with a new iteration and truncation scheme proposed recently. It is found for a cluster of 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1 approximately 7.4t, which is followed by another first-order transition to a 120 degrees Néel ordered state at Uc2 approximately 9.2t, where t is the transfer integral. The size dependence of the results is also addressed. Our results suggest the existence of the intermediate NMI phase and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions.
Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at Uc∼7.4tU_{\rm c} \sim 7.4tUc​∼7.4t , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.
We investigate the bandwidth-controlled Mott transition in the Hubbard model on the checkerboard lattice at half filling using the path-integral renormalization group (PIRG) method. It is demonstrated that the system undergoes a first-order phase transition to the plaquette-singlet insulating phase at a finite Hubbard interaction. This conclusion is drawn via a detailed analysis of the spin and charge correlations around the phase transition point by means of the PIRG method aided with a new iteration scheme introduced in this paper.
We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.
Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction UUU at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ (ttt being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For U>Uc2U>{U}_{\mathrm{c}2}U>Uc2​, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For Uc1<U<Uc2{U}_{\mathrm{c}1}<U<{U}_{\mathrm{c}2}Uc1​<U<Uc2​, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K\mathrm{K}K and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing UUU and thus the superconductivity is unlikely in the intermediate phase.
Antiferromagnetic and metal to insulator transitions in the ground state of two-dimensional half-filled and nearly half-filled Hubbard models with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Green's function approach with the self-energy up to the second order in the coupling constant U . For a choice of the parameter value t ′ / t =0.2 the half-filled model undergoes the first order phase transition between paramagnetic metallic (PM) phase and antiferromagnetic insulator (AFI) phase at U / t =4.0 while the first order transition between PM and antiferromagnetic metallic (AFM) phases takes place for nearly half-filled band. The one-electron spectral density is calculated for the PM, AFM, and AFI phases near the phase boundaries. In the PM phase the quasi-particle dispersion indicates the band narrowing from the Hartree-Fock results and the flat band behavior as was indicated by previous stadies and was observed in high- T c cuprates. The quasi-particle dispersion in the AFM phase is seen to be close to the Hartree-Fock results.