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:2407.11126 · Physical review. B./Physical review. B

Spontaneous layer selective Mott phase in the bilayer Hubbard model

Emile Pangburn, Louis Haurie, Sébastien Burdin, C. Pépin, Anurag Banerjee

Published Dec 19, 2024• 6 citations
arXivHTMLPDF

Abstract

Quantum materials featuring both itinerant and localized degrees of freedom exhibit numerous exotic phases and transitions that deviate from the Ginzburg-Landau paradigm. This paper uses the composite operator formalism to examine the bilayer strongly correlated Hubbard model. We observe the spontaneous breaking of layer symmetry, where the electron density in one of the layer reaches half-filling, resulting in a layer selective Mott phase (LSMP). This broken symmetry phase becomes unstable at a critical average electronic density away from half-filling. Furthermore, significant layer differentiation persists up to a moderate interlayer hopping, beyond which the system abruptly transitions to a layer uniform phase. In the LSMP phase, the electrons in the two layers are weakly hybridized, resulting in a small Fermi surface. The volume of the Fermi surface jumps at the transition from the LSMP to the uniform phase. We also discuss the physical mechanisms leading to the collapse of the LSMP phase under different perturbations.

DOI
10.1103/physrevb.110.235142

Related papers

Emergence of Kugel–Khomskii physics in quarter-filled bilayer correlated systems

Guijing Duan, Yangping Wang, Zhiguang Liao +2 more

Abstract We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of d z 2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel–Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.

Communications in Theoretical Physics•Mar 5, 2026•0 citations

Emergence of Kugel-Khomskii physics in quarter-filled bilayer correlated systems

Guijing Duan, Yunlong Wang, Zhiguang Liao +2 more

We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of dz2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel-Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.

arXiv:2601.06440•Jan 10, 2026•0 citations

Competition between band and Mott insulators in the bilayer Hubbard model: A dynamical cluster approximation study

Hunpyo Lee, Yu‐Zhong Zhang, Harald O. Jeschke +1 more

We investigate the nature of the insulating phases in a bilayer Hubbard model with intralayer coupling $t$ and interlayer coupling ${t}_{\ensuremath{\perp}}$ at large interaction strength $U/t$ and half-filling. We consider a dynamical cluster approximation with a cluster size of ${N}_{c}=2\ifmmode\times\else\texttimes\fi{}4$, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting (${t}_{\ensuremath{\perp}}/t$), we find that at ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}1.5$ the Mott behavior is rapidly suppressed in the momentum sectors ($\ensuremath{\pi},0$) and ($0,\ensuremath{\pi}$). At ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}2.5$, Mott features dominate in the momentum sectors ($\ensuremath{\pi},\ensuremath{\pi}$) of the bonding band and ($0,0$) of the antibonding band, and at ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}3.0$, a tiny scattering rate is observed in all momentum sectors at the Fermi level, indicating a transition from a Mott to a band insulator. We attribute such a momentum-dependent evolution of the insulating behavior to the competition and cooperation between short-range spatial fluctuations and interlayer coupling ${t}_{\ensuremath{\perp}}$ with the help of the Coulomb interaction $U$. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.

arXiv:1310.2821•Physical Review B•Jan 23, 2014•20 citations

Pair Structure and the Pairing Interaction in a Bilayer Hubbard Model

Thomas Maier, Douglas J. Scalapino

The bilayer Hubbard model with an intra-layer hopping $t$ and an inter-layer hopping $t_\perp$ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half-filling, if the splitting between the bonding and anti-bonding bands $t_\perp/t$ is small, the gap has $B_{1g}$ ($d_{x^2-y^2}$-wave) symmetry but when the splitting becomes larger, $A_{1g}$ ($s^\pm$-wave) pairing is favored. We also find that in the $s^\pm$ pairing region, the pairing is driven by inter-layer spin fluctuations and that $T_c$ is enhanced.

arXiv:1107.0401•Jul 2, 2011•1 citation

Band insulator to Mott insulator transition in a bilayer Hubbard model

S. S. Kancharla, Satoshi Okamoto

The ground-state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean-field theory. For weak to intermediate values of Coulomb repulsion $U$, the system undergoes a transition from a Mott-insulating phase to a metallic phase and then onto a band-insulating phase as the interlayer hopping is increased. In the strong-coupling case, the model exhibits a direct crossover from a Mott-insulating phase to a band-insulating phase. These results are robust with respect to the presence or absence of magnetic order.

arXiv:cond-mat/0703728•Physical Review B•May 15, 2007•86 citations

Charge density wave solutions of the Hubbard model in the composite operator formalism

Anurag Banerjee, Emile Pangburn, Chiranjit Mahato +2 more

We investigate the charge density wave phase in the strongly correlated Hubbard model without any other broken symmetry phase. Starting from the atomic Hamiltonian with no hopping, we generate quasiparticle operators corresponding to holons and doublons in the strongly correlated limit of the repulsive Hubbard model. We develop a real-space composite operator formalism using the equation of motion technique to include the intersite hopping perturbatively. Our fully self-consistent calculation stabilizes multiple unidirectional translation symmetry broken states within the doping range $\ensuremath{\delta}=0.07\ensuremath{-}0.2$. The charge-ordered states become increasingly unfavorable with hole doping. The unidirectional density waves manifest as periodic modulations of half-filled Mott regions separated by hole-rich regions. Notably, density wave solutions with periods of 3--8 lattice spacing remain energetically higher than those with larger periods. Quenched disorder on the charge-ordered states induces the merging of the Mott regions and, consequently, forms short-ranged charge modulations. The density of states shows signatures of strongly correlated Mott regions, potentially relevant to the physics of underdoped cuprates.

arXiv:2410.09903•Physical review. B./Physical review. B•Apr 14, 2025•4 citations
Quantum materials featuring both itinerant and localized degrees of freedom exhibit numerous exotic phases and transitions that deviate from the Ginzburg-Landau paradigm. This paper uses the composite operator formalism to examine the bilayer strongly correlated Hubbard model. We observe the spontaneous breaking of layer symmetry, where the electron density in one of the layer reaches half-filling, resulting in a layer selective Mott phase (LSMP). This broken symmetry phase becomes unstable at a critical average electronic density away from half-filling. Furthermore, significant layer differentiation persists up to a moderate interlayer hopping, beyond which the system abruptly transitions to a layer uniform phase. In the LSMP phase, the electrons in the two layers are weakly hybridized, resulting in a small Fermi surface. The volume of the Fermi surface jumps at the transition from the LSMP to the uniform phase. We also discuss the physical mechanisms leading to the collapse of the LSMP phase under different perturbations.
Abstract We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of d z 2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel–Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.
We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of dz2 orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel-Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.
We investigate the nature of the insulating phases in a bilayer Hubbard model with intralayer coupling ttt and interlayer coupling ${t}_{\ensuremath{\perp}}$ at large interaction strength U/tU/tU/t and half-filling. We consider a dynamical cluster approximation with a cluster size of ${N}_{c}=2\ifmmode\times\else\texttimes\fi{}4$, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting (${t}_{\ensuremath{\perp}}/t$), we find that at ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}1.5$ the Mott behavior is rapidly suppressed in the momentum sectors ($\ensuremath{\pi},0$) and ($0,\ensuremath{\pi}$). At ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}2.5$, Mott features dominate in the momentum sectors ($\ensuremath{\pi},\ensuremath{\pi}$) of the bonding band and (0,00,00,0) of the antibonding band, and at ${t}_{\ensuremath{\perp}}/t\ensuremath{\simeq}3.0$, a tiny scattering rate is observed in all momentum sectors at the Fermi level, indicating a transition from a Mott to a band insulator. We attribute such a momentum-dependent evolution of the insulating behavior to the competition and cooperation between short-range spatial fluctuations and interlayer coupling ${t}_{\ensuremath{\perp}}$ with the help of the Coulomb interaction UUU. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.
The bilayer Hubbard model with an intra-layer hopping ttt and an inter-layer hopping t⊥t_\perpt⊥​ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half-filling, if the splitting between the bonding and anti-bonding bands t⊥/tt_\perp/tt⊥​/t is small, the gap has B1gB_{1g}B1g​ (dx2−y2d_{x^2-y^2}dx2−y2​-wave) symmetry but when the splitting becomes larger, A1gA_{1g}A1g​ (s±s^\pms±-wave) pairing is favored. We also find that in the s±s^\pms± pairing region, the pairing is driven by inter-layer spin fluctuations and that TcT_cTc​ is enhanced.
The ground-state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean-field theory. For weak to intermediate values of Coulomb repulsion UUU, the system undergoes a transition from a Mott-insulating phase to a metallic phase and then onto a band-insulating phase as the interlayer hopping is increased. In the strong-coupling case, the model exhibits a direct crossover from a Mott-insulating phase to a band-insulating phase. These results are robust with respect to the presence or absence of magnetic order.
We investigate the charge density wave phase in the strongly correlated Hubbard model without any other broken symmetry phase. Starting from the atomic Hamiltonian with no hopping, we generate quasiparticle operators corresponding to holons and doublons in the strongly correlated limit of the repulsive Hubbard model. We develop a real-space composite operator formalism using the equation of motion technique to include the intersite hopping perturbatively. Our fully self-consistent calculation stabilizes multiple unidirectional translation symmetry broken states within the doping range $\ensuremath{\delta}=0.07\ensuremath{-}0.2$. The charge-ordered states become increasingly unfavorable with hole doping. The unidirectional density waves manifest as periodic modulations of half-filled Mott regions separated by hole-rich regions. Notably, density wave solutions with periods of 3--8 lattice spacing remain energetically higher than those with larger periods. Quenched disorder on the charge-ordered states induces the merging of the Mott regions and, consequently, forms short-ranged charge modulations. The density of states shows signatures of strongly correlated Mott regions, potentially relevant to the physics of underdoped cuprates.