Interior-gap superconductivity has long been discussed as an exotic paired state in the presence of Fermi-surface mismatch, but its realization in canonical strongly correlated models has remained elusive. Here we present evidence that the superconducting phase of one-dimensional Kondo-Heisenberg models realizes an interior-gap pair-density-wave (PDW) state generated by strong correlations. Combining infinite density-matrix-renormalization-group (iDMRG) and finite DMRG calculations for $S=1/2$ and $S=3/2$ chains, we show that the PDW correlation is the dominant bulk superconducting correlation in the spin-gapped regime and that the momentum distribution function $n(k)$ exhibits a reconstructed structure characteristic of interior-gap physics. In particular, while the feature in $n(k)$ for the $S=1/2$ chain is only hump-like, the corresponding structure in the $S=3/2$ chain develops into a clear dip, strongly supporting the interpretation in terms of an interior-gap-like dip structure. Unlike conventional interior-gap scenarios based on a mismatch between preexisting Fermi surfaces, the present system starts from a single bare conduction-electron Fermi surface, and the additional low-energy single-particle structure emerges dynamically together with the dominant PDW correlation through the Kondo coupling. Finite DMRG data further demonstrate that boundary effects can substantially modify real-space correlations in this gapless one-dimensional system, making a direct thermodynamic-limit calculation essential for identifying the intrinsic bulk momentum structure and the dominant correlation channel.Interior-gap superconductivity has long been discussed as an exotic paired state in the presence of Fermi-surface mismatch, but its realization in canonical strongly correlated models has remained elusive. Here we present evidence that the superconducting phase of one-dimensional Kondo-Heisenberg models realizes an interior-gap pair-density-wave (PDW) state generated by strong correlations. Combining infinite density-matrix-renormalization-group (iDMRG) and finite DMRG calculations for $S=1/2$ and $S=3/2$ chains, we show that the PDW correlation is the dominant bulk superconducting correlation in the spin-gapped regime and that the momentum distribution function $n(k)$ exhibits a reconstructed structure characteristic of interior-gap physics. In particular, while the feature in $n(k)$ for the $S=1/2$ chain is only hump-like, the corresponding structure in the $S=3/2$ chain develops into a clear dip, strongly supporting the interpretation in terms of an interior-gap-like dip structure. Unlike conventional interior-gap scenarios based on a mismatch between preexisting Fermi surfaces, the present system starts from a single bare conduction-electron Fermi surface, and the additional low-energy single-particle structure emerges dynamically together with the dominant PDW correlation through the Kondo coupling. Finite DMRG data further demonstrate that boundary effects can substantially modify real-space correlations in this gapless one-dimensional system, making a direct thermodynamic-limit calculation essential for identifying the intrinsic bulk momentum structure and the dominant correlation channel.

arXiv:2604.27440Apr 30, 20260 citations

Propagation of local excitations through strongly correlated quantum chains

J. Richert, Tarek Khalil

arXiv:1109.3392Physica B Condensed MatterDec 9, 20113 citations

Quantum Transport in Strongly Correlated Systems

Rudi Malfliet

Jan 1, 19980 citations

Strong Correlation in Molecular Periodic Systems from a Variational Reduced Density Matrix Theory

Simon Ewing, David A. Mazziotti

Molecular periodic systems have the challenge of not only representing an infinite, albeit periodically repeating, molecule but also treating the strong electron correlation that emerges in such systems. Many post-Hartree-Fock methods that are efficient in moderately correlated molecules often fail to describe strongly correlated electrons and their properties in periodic systems. Here we develop and apply an electronic structure approach to periodic systems based on the variational calculation of the two-electron reduced density matrix (2-RDM). The variational 2-RDM method calculates a lower bound to the ground-state energy of a molecular periodic system without computation or storage of its many-electron wave function. The 2-RDM is constrained by $N$ -representability conditions that are necessary for it to represent at least one $N$ -electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.Molecular periodic systems have the challenge of not only representing an infinite, albeit periodically repeating, molecule but also treating the strong electron correlation that emerges in such systems. Many post-Hartree-Fock methods that are efficient in moderately correlated molecules often fail to describe strongly correlated electrons and their properties in periodic systems. Here we develop and apply an electronic structure approach to periodic systems based on the variational calculation of the two-electron reduced density matrix (2-RDM). The variational 2-RDM method calculates a lower bound to the ground-state energy of a molecular periodic system without computation or storage of its many-electron wave function. The 2-RDM is constrained by $N$-representability conditions that are necessary for it to represent at least one $N$-electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.

Aug 6, 20202 citations

Correlated States of Quantum Chain

Olga V. Man’ko

Springer eBooksApr 7, 20080 citations

Enhanced superconductivity by near-neighbor attraction in the doped extended Hubbard model

Cheng Peng, Yao Wang, Jiajia Wen +3 more

A recent experiment has unveiled an anomalously strong electron-electron attraction in the one-dimensional copper-oxide chain ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$. While the effect of the near-neighbor electron attraction $V$ in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction $V$ can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.A recent experiment has unveiled an anomalously strong electron-electron attraction in the one-dimensional copper-oxide chain ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$. While the effect of the near-neighbor electron attraction $V$ in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction $V$ can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.

arXiv:2206.03486Physical review. B./Physical review. BMay 3, 202342 citations

S=1/2

and

S=3/2

chains, we show that the PDW correlation is the dominant bulk superconducting correlation in the spin-gapped regime and that the momentum distribution function

n(k)

exhibits a reconstructed structure characteristic of interior-gap physics. In particular, while the feature in

n(k)

for the

S=1/2

chain is only hump-like, the corresponding structure in the

S=3/2

chain develops into a clear dip, strongly supporting the interpretation in terms of an interior-gap-like dip structure. Unlike conventional interior-gap scenarios based on a mismatch between preexisting Fermi surfaces, the present system starts from a single bare conduction-electron Fermi surface, and the additional low-energy single-particle structure emerges dynamically together with the dominant PDW correlation through the Kondo coupling. Finite DMRG data further demonstrate that boundary effects can substantially modify real-space correlations in this gapless one-dimensional system, making a direct thermodynamic-limit calculation essential for identifying the intrinsic bulk momentum structure and the dominant correlation channel.

N

-representability conditions that are necessary for it to represent at least one

N

-electron density matrix---conditions that allow it to treat strongly correlated systems. Two periodic systems are treated to demonstrate the methodology: (i) a metallic hydrogen chain and (ii) a strongly correlated acene chain. In the hydrogen chains the 2-RDM theory describes the strongly correlated Mott metal-to-insulator transition while in acene chains it describes the emergence of polyradical character with increasing chain length. The methodology is applicable to treating strong electron correlation in more general periodic molecules and materials.

V

in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction

V

can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.