Physical review. B./Physical review. B

Strong pairing and symmetric pseudogap metal in a double Kondo lattice model: From a nickelate superconductor to a tetralayer optical lattice

Hui Yang, Hanbit Oh, Ya-Hui Zhang

Published Jun 2, 2025• 9 citations

Abstract

In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice models in two separate layers, with Kondo coupling ${J}_{K}$ within each layer, while the localized spin moments are coupled together via an interlayer on-site antiferromagnetic spin coupling ${J}_{\ensuremath{\perp}}$. We consider the strong ${J}_{\ensuremath{\perp}}$ limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling ${J}_{K}$ transmits the interlayer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong interlayer antiferromangetic spin coupling and form strong interlayer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ limits of the model describes the recently found bilayer nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, while the ${J}_{K}>0$ side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ and ${J}_{K}\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of ${J}_{K}$. We highlight both the qualitative similarity and the quantitative difference in the two sides of ${J}_{K}$. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

DOI: 10.1103/physrevb.111.l241102

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Strong pairing and symmetric pseudogap metal in double Kondo lattice model: from nickelate superconductor to tetralayer optical lattice

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Intertwined Superconductivity and Magnetism from Repulsive Interactions in Kondo Bilayers

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

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cond-mat.quant-gasCross-listedarXiv:2512.09926Dec 11, 20250 citations

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arXiv:2602.10091Feb 10, 20260 citations

Physical review. B./Physical review. B

Strong pairing and symmetric pseudogap metal in a double Kondo lattice model: From a nickelate superconductor to a tetralayer optical lattice

Hui Yang, Hanbit Oh, Ya-Hui Zhang

Published Jun 2, 2025• 9 citations

Publisher

Abstract

{J}_{K}

within each layer, while the localized spin moments are coupled together via an interlayer on-site antiferromagnetic spin coupling

{J}_{\ensuremath{\perp}}

. We consider the strong

{J}_{\ensuremath{\perp}}

limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling

{J}_{K}

transmits the interlayer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong interlayer antiferromangetic spin coupling and form strong interlayer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the

{J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}

limits of the model describes the recently found bilayer nickelate

{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}

, while the

{J}_{K}>0

side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits,

{J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}

and

{J}_{K}\ensuremath{\rightarrow}+\ensuremath{\infty}

limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of

{J}_{K}

. We highlight both the qualitative similarity and the quantitative difference in the two sides of

{J}_{K}

. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

DOI: 10.1103/physrevb.111.l241102

Related papers

Strong pairing and symmetric pseudogap metal in double Kondo lattice model: from nickelate superconductor to tetralayer optical lattice

Hui Yang, Hanbit Oh, Ya-Hui Zhang

In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice model, each with Kondo coupling $J_K$ within each layer, while the localized spin moments are coupled together via an inter-layer on-site antiferromagnetic spin coupling $J_\perp$ . We consider the strong $J_\perp$ limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling $J_K$ transmits the inter-layer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong inter-layer antiferromangetic spin coupling and form strong inter-layer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the $J_K \rightarrow -\infty$ limits of the model describes the recently found bilayer nickelate La $_3$ Ni $_2$ O $_7$ , while the $J_K>0$ side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, $J_K \rightarrow -\infty$ and $J_K \rightarrow +\infty$ limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of $J_K$ . We highlight both the qualitative similarity and the quantitative difference in the two sides of $J_K$ . Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice model, each with Kondo coupling $J_K$ within each layer, while the localized spin moments are coupled together via an inter-layer on-site antiferromagnetic spin coupling $J_\perp$. We consider the strong $J_\perp$ limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling $J_K$ transmits the inter-layer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong inter-layer antiferromangetic spin coupling and form strong inter-layer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the $J_K \rightarrow -\infty$ limits of the model describes the recently found bilayer nickelate La$_3$Ni$_2$O$_7$, while the $J_K>0$ side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, $J_K \rightarrow -\infty$ and $J_K \rightarrow +\infty$ limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of $J_K$. We highlight both the qualitative similarity and the quantitative difference in the two sides of $J_K$. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

arXiv:2408.01493Aug 2, 20240 citations

Doping a spin-one Mott insulator: possible application to bilayer nickelate

Hanbit Oh, Hui Yang, Ya-Hui Zhang

Abstract In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the d 8 valence. These studies are particularly relevant—though not limited—to the recently discovered bilayer nickelate superconductor La 3 Ni 2 O 7 . We focus on a ferromagnetic Kondo lattice model with mobile electrons in the d x 2 − y 2 orbital coupled to the localized spin moments in d z 2 orbital through a large Hund’s coupling J H . In the large J H limit, the model reduces to the type II t − J model with a mixture of spin-half singlon states and spin-one doublon states. We summarize density matrix renormalization group results on the Luther-Emery liquid in one dimensional chain and two-leg ladder. Then we mainly focus on bilayer square lattice and show that a large inter-layer coupling J ⊥ of d z 2 orbital can induce strong inter-layer pairing of d x 2 − y 2 orbital. In the strong J ⊥ limit, a kinetic-energy driven high T c superconductivity is demonstrated in an ideal model with only a single hopping term. Furthermore, the model predicts a symmetric pseudogap metal—dubbed ‘second Fermi liquid (FL)’—in the underdoped regime, yielding a phase diagram analogous to that of hole-doped cuprates. The bilayer Kondo model therefore presents a promising platform for both realizing higher- T c superconductors and exploring non-FL physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.Abstract In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the d 8 valence. These studies are particularly relevant—though not limited—to the recently discovered bilayer nickelate superconductor La 3 Ni 2 O 7 . We focus on a ferromagnetic Kondo lattice model with mobile electrons in the d x 2 − y 2 orbital coupled to the localized spin moments in d z 2 orbital through a large Hund’s coupling J H . In the large J H limit, the model reduces to the type II t − J model with a mixture of spin-half singlon states and spin-one doublon states. We summarize density matrix renormalization group results on the Luther-Emery liquid in one dimensional chain and two-leg ladder. Then we mainly focus on bilayer square lattice and show that a large inter-layer coupling J ⊥ of d z 2 orbital can induce strong inter-layer pairing of d x 2 − y 2 orbital. In the strong J ⊥ limit, a kinetic-energy driven high T c superconductivity is demonstrated in an ideal model with only a single hopping term. Furthermore, the model predicts a symmetric pseudogap metal—dubbed ‘second Fermi liquid (FL)’—in the underdoped regime, yielding a phase diagram analogous to that of hole-doped cuprates. The bilayer Kondo model therefore presents a promising platform for both realizing higher- T c superconductors and exploring non-FL physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.

arXiv:2509.02673New Journal of PhysicsJan 26, 20263 citations

Intertwined Superconductivity and Magnetism from Repulsive Interactions in Kondo Bilayers

Clara S. Weber, Dominik Kiese, Dante Marvin Kennes +1 more

While superconductors are conventionally established by attractive interactions, higher-temperature mechanisms for emergent electronic pairing from strong repulsive electron-electron interactions remain under considerable scrutiny. Here, we establish a strong-coupling mechanism for intertwined superconductivity and magnetic order from purely repulsive interactions in a Kondo-like bilayer system, composed of a two-dimensional Mott insulator coupled to a layer of weakly-interacting itinerant electrons. Combining large scale DMRG and Monte Carlo simulations, we find that superconductivity persists and coexists with magnetism over a wide range of interlayer couplings. We classify the resulting rich phase diagram and find 2-rung antiferromagnetic and 4-rung antiferromagnetic order in one-dimensional systems along with a phase separation regime, while finding that superconductivity coexists with either antiferromagnetic or ferromagnetic order in two dimensions. Remarkably, the model permits a rigorous strong-coupling analysis via localized spins coupled to charge-2e bosons through Kugel-Khomskii interactions, capturing the pairing mechanism in the presence of magnetism due to emergent attractive interactions. Our numerical analysis reveals that pairing remains robust well beyond the strong-coupling regime, establishing a new mechanism for superconductivity in coupled weakly- and strongly-interacting electron systems, relevant for infinite-layer nickelates and superconductivity in moire multilayer heterostructures.While superconductors are conventionally established by attractive interactions, higher-temperature mechanisms for emergent electronic pairing from strong repulsive electron-electron interactions remain under considerable scrutiny. Here, we establish a strong-coupling mechanism for intertwined superconductivity and magnetic order from purely repulsive interactions in a Kondo-like bilayer system, composed of a two-dimensional Mott insulator coupled to a layer of weakly-interacting itinerant electrons. Combining large scale DMRG and Monte Carlo simulations, we find that superconductivity persists and coexists with magnetism over a wide range of interlayer couplings. We classify the resulting rich phase diagram and find 2-rung antiferromagnetic and 4-rung antiferromagnetic order in one-dimensional systems along with a phase separation regime, while finding that superconductivity coexists with either antiferromagnetic or ferromagnetic order in two dimensions. Remarkably, the model permits a rigorous strong-coupling analysis via localized spins coupled to charge-2e bosons through Kugel-Khomskii interactions, capturing the pairing mechanism in the presence of magnetism due to emergent attractive interactions. Our numerical analysis reveals that pairing remains robust well beyond the strong-coupling regime, establishing a new mechanism for superconductivity in coupled weakly- and strongly-interacting electron systems, relevant for infinite-layer nickelates and superconductivity in moire multilayer heterostructures.

arXiv:2408.02847Aug 5, 20240 citations

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.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:2307.16873Physical Review LettersJan 19, 2024187 citations

Connecting single-layer $t$ - $J$ to Kondo lattice models: Exploration with cold atomsConnecting single-layer $t$-$J$ to Kondo lattice models: Exploration with cold atoms

Hannah Lange, Eugene Demler, Jan von Delft +2 more

The Kondo effect, a hallmark of many-body physics, emerges from the antiferromagnetic coupling between localized spins and conduction fermions, leading to a correlated many-body singlet state. Here we propose to use the mixed-dimensional (mixD) bilayer Hubbard geometry as a platform to study Kondo lattice physics with current ultracold atom experiments. At experimentally feasible temperatures, we predict that key features of the Kondo effect can be observed, including formation of the Kondo cloud around a single impurity and the competition of singlet formation with Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for multiple impurities, summarized in the Doniach phase diagram. Moreover, we show that the mixD platform provides a natural bridge between the Doniach phase diagram of the Kondo lattice model, relevant to heavy-fermion materials, and the phase diagram of cuprate superconductors as described by a single-layer Zhang-Rice type $t$ - $J$ model: It is possible to continuously tune between the two regimes by changing the interlayer Kondo coupling. Our findings demonstrate that the direct connection between high-temperature superconductivity and heavy-fermion physics can be experimentally studied using currently available quantum simulation platforms.The Kondo effect, a hallmark of many-body physics, emerges from the antiferromagnetic coupling between localized spins and conduction fermions, leading to a correlated many-body singlet state. Here we propose to use the mixed-dimensional (mixD) bilayer Hubbard geometry as a platform to study Kondo lattice physics with current ultracold atom experiments. At experimentally feasible temperatures, we predict that key features of the Kondo effect can be observed, including formation of the Kondo cloud around a single impurity and the competition of singlet formation with Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for multiple impurities, summarized in the Doniach phase diagram. Moreover, we show that the mixD platform provides a natural bridge between the Doniach phase diagram of the Kondo lattice model, relevant to heavy-fermion materials, and the phase diagram of cuprate superconductors as described by a single-layer Zhang-Rice type $t$-$J$ model: It is possible to continuously tune between the two regimes by changing the interlayer Kondo coupling. Our findings demonstrate that the direct connection between high-temperature superconductivity and heavy-fermion physics can be experimentally studied using currently available quantum simulation platforms.

cond-mat.quant-gasCross-listedarXiv:2512.09926Dec 11, 20250 citations

Simulating superconductivity in mixed-dimensional $t_\parallel$ - ${J}_\parallel$ - ${J}_\perp$ bilayers with neural quantum statesSimulating superconductivity in mixed-dimensional $t_\parallel$-${J}_\parallel$-${J}_\perp$ bilayers with neural quantum states

Hannah Lange, Ao Chen, Antoine Georges +3 more

Motivated by the recent discovery of superconductivity in the bilayer nickelate La $_3$ Ni $_2$ O $_7$ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer $t_\parallel$ - $J_\parallel$ - $J_\perp$ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to $8\times 8\times 2$ sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer $s$ -wave pairing to intralayer $d$ -wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.Motivated by the recent discovery of superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer $t_\parallel$-$J_\parallel$-$J_\perp$ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to $8\times 8\times 2$ sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer $s$-wave pairing to intralayer $d$-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.

arXiv:2602.10091Feb 10, 20260 citations

{J}_{K}

within each layer, while the localized spin moments are coupled together via an interlayer on-site antiferromagnetic spin coupling

{J}_{\ensuremath{\perp}}

. We consider the strong

{J}_{\ensuremath{\perp}}

limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling

{J}_{K}

{J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}

limits of the model describes the recently found bilayer nickelate

{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}

, while the

{J}_{K}>0

side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits,

{J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}

and

{J}_{K}\ensuremath{\rightarrow}+\ensuremath{\infty}

{J}_{K}

. We highlight both the qualitative similarity and the quantitative difference in the two sides of

{J}_{K}

. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice model, each with Kondo coupling

J_K

within each layer, while the localized spin moments are coupled together via an inter-layer on-site antiferromagnetic spin coupling

J_\perp

. We consider the strong

J_\perp

limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling

J_K

transmits the inter-layer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong inter-layer antiferromangetic spin coupling and form strong inter-layer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the

J_K \rightarrow -\infty

limits of the model describes the recently found bilayer nickelate La

_3

_2

_7

, while the

J_K>0

side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits,

J_K \rightarrow -\infty

and

J_K \rightarrow +\infty

J_K

. We highlight both the qualitative similarity and the quantitative difference in the two sides of

J_K

. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

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.

Connecting single-layer

t

J

to Kondo lattice models: Exploration with cold atoms

t

J

model: It is possible to continuously tune between the two regimes by changing the interlayer Kondo coupling. Our findings demonstrate that the direct connection between high-temperature superconductivity and heavy-fermion physics can be experimentally studied using currently available quantum simulation platforms.

Simulating superconductivity in mixed-dimensional

t_\parallel

{J}_\parallel

{J}_\perp

bilayers with neural quantum states

Motivated by the recent discovery of superconductivity in the bilayer nickelate La

_3

_2

_7

(LNO) under pressure, we study a mixed-dimensional (mixD) bilayer

t_\parallel

J_\parallel

J_\perp

model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to

8\times 8\times 2

sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer

s

-wave pairing to intralayer

d

-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.