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:2411.13399 · Physical review. B./Physical review. B

Numerical study of the bilayer two-orbital model for La 3 Ni 2 O 7 on a plaquette ladder

Yang Shen, Jiale Huang, Xiangjian Qian, Guang-Ming Zhang, Mingpu Qin

Published May 23, 2025• 5 citations
arXivHTMLPDF

Abstract

The recently discovered high-${T}_{c}$ superconductivity in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ with ${T}_{c}\ensuremath{\approx}80$ K provides another intriguing platform to explore the microscopic mechanism of unconventional superconductivity. In this work, we study a previously proposed bilayer two-orbital model Hamiltonian for ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ [Y. Shen et al., Chin. Phys. Lett. 40, 127401 (2023)] on a plaquette ladder, which is a minimum setup with two-dimensional characteristic. We employ large-scale density matrix renormalization group calculations to accurately determine the ground state of the model. We determine the density, magnetic structure, and the pairing property of the model. We find that with large effective interlayer antiferromagnetic exchange for the $3{d}_{{z}^{2}}$ orbital, the spin, charge, and pairing correlation display quasi-long-range behavior, which could be viewed as a precursor of possible true long-range order in the two-dimensional limit. Interestingly, sign oscillation for the pairing correlation is observed for both the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and $3{d}_{{z}^{2}}$ orbitals, indicating the presence of a possible pair density wave in the system. Even though we only study the model on a quasi-one-dimensional plaquette ladder geometry due to the computational difficulty, the results for the spin, charge, and pairing correlation provide valuable insight towards the clarification of the properties of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$.

DOI
10.1103/physrevb.111.l180508

Related papers

Bilayer t − J − J ⊥ Model and Magnetically Mediated Pairing in the Pressurized Nickelate La 3 Ni 2 O 7

Xing-Zhou Qu, Dai-Wei Qu, Jialin Chen +4 more

The recently discovered nickelate superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ has a high transition temperature near 80 K under pressure, providing an additional avenue for exploring unconventional superconductivity. Here, with state-of-the-art tensor-network methods, we study a bilayer ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model for ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ and find a robust $s$-wave superconductive (SC) order mediated by interlayer magnetic couplings. Large-scale density matrix renormalization group calculations find algebraic pairing correlations with Luttinger parameter ${K}_{\mathrm{SC}}\ensuremath{\lesssim}1$. Infinite projected entangled-pair state method obtains a nonzero SC order directly in the thermodynamic limit, and estimates a strong pairing strength ${\overline{\mathrm{\ensuremath{\Delta}}}}_{z}\ensuremath{\sim}\mathcal{O}(0.1)$. Tangent-space tensor renormalization group simulations elucidate the temperature evolution of SC pairing and further determine a high SC temperature ${T}_{c}^{*}/J\ensuremath{\sim}\mathcal{O}(0.1)$. Because of the intriguing orbital selective behaviors and strong Hund's rule coupling in the compound, ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model has strong interlayer spin exchange (while negligible interlayer hopping), which greatly enhances the SC pairing in the bilayer system. Such a magnetically mediated pairing has also been observed recently in the optical lattice of ultracold atoms. Our accurate and comprehensive tensor-network calculations reveal a robust SC order in the bilayer ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model and shed light on the pairing mechanism of the high-${T}_{c}$ nickelate superconductor.

arXiv:2307.16873•Physical Review Letters•Jan 19, 2024•187 citations

Pair correlations in the two-orbital Hubbard ladder: Implications for superconductivity in the bilayer nickelate La3Ni2O7

Tatsuya Kaneko, Hirofumi Sakakibara, Masayuki Ochi +1 more

Motivated by high-temperature superconductivity in pressurized ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, we investigate the pair correlations in the two-orbital Hubbard ladder, which consists of the nearly half-filled and nearly quarter-filled orbitals. By employing the density matrix renormalization group method, we demonstrate that the pair correlation exhibits a power-law decay against the distance while the spin correlation decays exponentially. The decay exponent of the pair correlation of the nearly half-filled orbital is comparable to the exponent of the quasi-long-range superconducting correlation in the doped single-orbital Hubbard ladder, which suggests the importance of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$.

arXiv:2310.01952•Physical review. B./Physical review. B•Jan 31, 2024•60 citations

Feshbach resonance in a strongly repulsive ladder of mixed dimensionality: A possible scenario for bilayer nickelate superconductors

Hannah Lange, Lukas Homeier, Eugene Demler +3 more

Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-${T}_{c}$ superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under pressure, we study a minimal bilayer model, in which, as in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, interlayer and intralayer magnetic interactions but no interlayer hopping are present: A mixed-dimensional (mixD) $t\text{\ensuremath{-}}J$ model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: From a closed-channel-dominated regime of tightly bound bosonic pairs of holes to an open-channel-dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion $V$ that we include in our model. Using density matrix renormalization group simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling $\ensuremath{\delta}=0.5$ at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is lowered in energy by doping or tuning $V$, a Feshbach resonance is realized, associated with a dome in the binding energy. Our predictions can be directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$.

Physical review. B./Physical review. B•Jan 16, 2024•40 citations

Pair correlations of the hybridized orbitals in a ladder model for the bilayer nickelate La 3 Ni 2 O 7

Masataka Kakoi, Tatsuya Kaneko, Hirofumi Sakakibara +2 more

To clarify the nature of high-temperature superconductivity in the bilayer nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under pressure, we investigate, using the density-matrix renormalization group method, the pair correlations in the two-orbital $t\text{\ensuremath{-}}J$ ladder model. While the interchain-intraorbital pair correlations exhibit a slow power-law decay in both orbitals, the interorbital pair correlation also develops strongly enough to be comparable with the intraorbital correlations. These intra and interorbital pair correlations are enhanced by Hund's coupling, but more importantly, the interorbital pair correlation develops even when interorbital pairing glue mediated by Hund's coupling is absent. Our finding suggests that the pair correlation in the present system develops as a hybridized two-orbital entity, which may have some implications on the superconductivity in the bilayer nickelate.

arXiv:2312.04304•Physical review. B./Physical review. B•May 24, 2024•38 citations

Extended s -wave pairing from an emergent Feshbach resonance in bilayer nickelate superconductors

Pietro Borchia, Hannah Lange, Fabian Grusdt

Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high- T c superconductivity in nickelate bilayer La 3 Ni 2 O 7 (LNO), we study a minimal mixed dimensional t − J model supplemented with a repulsive Coulomb interaction V . When hole doped, previous numerical simulations revealed that the system exhibits strong binding energies, with a phenomenology resembling a BCS-to-BEC crossover accompanied by a Feshbach resonance between two distinct types of charge carriers. Here, we perform a mean-field analysis that enables a direct observation of the BCS-to-BEC crossover as well as microscopic insights into the crossover region and the pairing symmetry for two-dimensional bilayers. We benchmark our mean-field description by comparing it to density-matrix renormalization group simulations in quasi-one-dimensional settings and find remarkably good agreement. For the two-dimensional system relevant to LNO, our mean-field calculations predict a BCS pairing gap with an extended s -wave symmetry, directly resulting from the pairing mechanism's Feshbach origin. Our analysis hence gives insights into pairing in unconventional superconductors and, further, can be tested in currently available ultracold atom experiments.

arXiv:2502.13960•Physical review. B./Physical review. B•Oct 10, 2025•2 citations

Evolution from intralayer to interlayer superconductivity in a bilayer $t$-$J$ model

Yang, Yuan, Xin Lu, Yuan Wan +2 more

Motivated by the bilayer cuprate superconductors and nickelate superconductor La$_3$Ni$_2$O$_7$, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg $t$-$J$-$J_{\bot}$ model, where $t$ is the in-plane electron hopping, $J$ is the in-plane spin interaction, and $J_{\bot}$ is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning $J_{\bot}$ in a large doping range $δ= 1/8 - 1/2$. We find that a large $J_{\bot}$ can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at $δ= 1/4$. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large $J_{\bot}$, as reported in previous literature. Interestingly, in the intermediate $J_{\bot}$ regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent $K^{zz}_{\rm SC} \sim 1$. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg $t$-$J$ ladders by a strong $J_{\bot}$ interaction, from both the Luther-Emery liquid and Luttinger-liquid states.

arXiv:2507.07545•Jul 10, 2025•0 citations
The recently discovered high-Tc{T}_{c}Tc​ superconductivity in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ with Tc\ensuremath≈80{T}_{c}\ensuremath{\approx}80Tc​\ensuremath≈80 K provides another intriguing platform to explore the microscopic mechanism of unconventional superconductivity. In this work, we study a previously proposed bilayer two-orbital model Hamiltonian for La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ [Y. Shen et al., Chin. Phys. Lett. 40, 127401 (2023)] on a plaquette ladder, which is a minimum setup with two-dimensional characteristic. We employ large-scale density matrix renormalization group calculations to accurately determine the ground state of the model. We determine the density, magnetic structure, and the pairing property of the model. We find that with large effective interlayer antiferromagnetic exchange for the 3dz23{d}_{{z}^{2}}3dz2​ orbital, the spin, charge, and pairing correlation display quasi-long-range behavior, which could be viewed as a precursor of possible true long-range order in the two-dimensional limit. Interestingly, sign oscillation for the pairing correlation is observed for both the 3dx2\ensuremath−y23{d}_{{x}^{2}\ensuremath{-}{y}^{2}}3dx2\ensuremath−y2​ and 3dz23{d}_{{z}^{2}}3dz2​ orbitals, indicating the presence of a possible pair density wave in the system. Even though we only study the model on a quasi-one-dimensional plaquette ladder geometry due to the computational difficulty, the results for the spin, charge, and pairing correlation provide valuable insight towards the clarification of the properties of La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
The recently discovered nickelate superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ has a high transition temperature near 80 K under pressure, providing an additional avenue for exploring unconventional superconductivity. Here, with state-of-the-art tensor-network methods, we study a bilayer ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model for La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ and find a robust sss-wave superconductive (SC) order mediated by interlayer magnetic couplings. Large-scale density matrix renormalization group calculations find algebraic pairing correlations with Luttinger parameter ${K}_{\mathrm{SC}}\ensuremath{\lesssim}1$. Infinite projected entangled-pair state method obtains a nonzero SC order directly in the thermodynamic limit, and estimates a strong pairing strength ${\overline{\mathrm{\ensuremath{\Delta}}}}_{z}\ensuremath{\sim}\mathcal{O}(0.1)$. Tangent-space tensor renormalization group simulations elucidate the temperature evolution of SC pairing and further determine a high SC temperature ${T}_{c}^{*}/J\ensuremath{\sim}\mathcal{O}(0.1)$. Because of the intriguing orbital selective behaviors and strong Hund's rule coupling in the compound, ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model has strong interlayer spin exchange (while negligible interlayer hopping), which greatly enhances the SC pairing in the bilayer system. Such a magnetically mediated pairing has also been observed recently in the optical lattice of ultracold atoms. Our accurate and comprehensive tensor-network calculations reveal a robust SC order in the bilayer ${t\text{\ensuremath{-}}J\text{\ensuremath{-}}J}_{\ensuremath{\perp}}$ model and shed light on the pairing mechanism of the high-Tc{T}_{c}Tc​ nickelate superconductor.
Motivated by high-temperature superconductivity in pressurized La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​, we investigate the pair correlations in the two-orbital Hubbard ladder, which consists of the nearly half-filled and nearly quarter-filled orbitals. By employing the density matrix renormalization group method, we demonstrate that the pair correlation exhibits a power-law decay against the distance while the spin correlation decays exponentially. The decay exponent of the pair correlation of the nearly half-filled orbital is comparable to the exponent of the quasi-long-range superconducting correlation in the doped single-orbital Hubbard ladder, which suggests the importance of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-Tc{T}_{c}Tc​ superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ under pressure, we study a minimal bilayer model, in which, as in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​, interlayer and intralayer magnetic interactions but no interlayer hopping are present: A mixed-dimensional (mixD) $t\text{\ensuremath{-}}J$ model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: From a closed-channel-dominated regime of tightly bound bosonic pairs of holes to an open-channel-dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion VVV that we include in our model. Using density matrix renormalization group simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling $\ensuremath{\delta}=0.5$ at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is lowered in energy by doping or tuning VVV, a Feshbach resonance is realized, associated with a dome in the binding energy. Our predictions can be directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
To clarify the nature of high-temperature superconductivity in the bilayer nickelate La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ under pressure, we investigate, using the density-matrix renormalization group method, the pair correlations in the two-orbital $t\text{\ensuremath{-}}J$ ladder model. While the interchain-intraorbital pair correlations exhibit a slow power-law decay in both orbitals, the interorbital pair correlation also develops strongly enough to be comparable with the intraorbital correlations. These intra and interorbital pair correlations are enhanced by Hund's coupling, but more importantly, the interorbital pair correlation develops even when interorbital pairing glue mediated by Hund's coupling is absent. Our finding suggests that the pair correlation in the present system develops as a hybridized two-orbital entity, which may have some implications on the superconductivity in the bilayer nickelate.
Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high- T c superconductivity in nickelate bilayer La 3 Ni 2 O 7 (LNO), we study a minimal mixed dimensional t − J model supplemented with a repulsive Coulomb interaction V . When hole doped, previous numerical simulations revealed that the system exhibits strong binding energies, with a phenomenology resembling a BCS-to-BEC crossover accompanied by a Feshbach resonance between two distinct types of charge carriers. Here, we perform a mean-field analysis that enables a direct observation of the BCS-to-BEC crossover as well as microscopic insights into the crossover region and the pairing symmetry for two-dimensional bilayers. We benchmark our mean-field description by comparing it to density-matrix renormalization group simulations in quasi-one-dimensional settings and find remarkably good agreement. For the two-dimensional system relevant to LNO, our mean-field calculations predict a BCS pairing gap with an extended s -wave symmetry, directly resulting from the pairing mechanism's Feshbach origin. Our analysis hence gives insights into pairing in unconventional superconductors and, further, can be tested in currently available ultracold atom experiments.
Evolution from intralayer to interlayer superconductivity in a bilayer ttt-JJJ model
Motivated by the bilayer cuprate superconductors and nickelate superconductor La3_33​Ni2_22​O7_77​, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg ttt-JJJ-J⊥J_{\bot}J⊥​ model, where ttt is the in-plane electron hopping, JJJ is the in-plane spin interaction, and J⊥J_{\bot}J⊥​ is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning J⊥J_{\bot}J⊥​ in a large doping range δ=1/8−1/2δ= 1/8 - 1/2δ=1/8−1/2. We find that a large J⊥J_{\bot}J⊥​ can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at δ=1/4δ= 1/4δ=1/4. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large J⊥J_{\bot}J⊥​, as reported in previous literature. Interestingly, in the intermediate J⊥J_{\bot}J⊥​ regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent KSCzz∼1K^{zz}_{\rm SC} \sim 1KSCzz​∼1. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg ttt-JJJ ladders by a strong J⊥J_{\bot}J⊥​ interaction, from both the Luther-Emery liquid and Luttinger-liquid states.