The effect of strong anisotropy on the Fermi line of a system of correlated electrons is studied in two space dimensions using renormalization group techniques. Inflection points change the scaling exponents of the couplings and enhance the instabilities of the system. They increase the critical dimension for non-Fermi-liquid behavior from 1 to 3/2. Assuming that, in the absence of nesting, the dominant instability is towards a superconducting ground state, simple rules to discern between d-wave and extended s-wave symmetry of the order parameter are given.The effect of strong anisotropy on the Fermi line of a system of correlated electrons is studied in two space dimensions using renormalization group techniques. Inflection points change the scaling exponents of the couplings and enhance the instabilities of the system. They increase the critical dimension for non-Fermi-liquid behavior from 1 to 3/2. Assuming that, in the absence of nesting, the dominant instability is towards a superconducting ground state, simple rules to discern between d-wave and extended s-wave symmetry of the order parameter are given.

arXiv:cond-mat/9703254Physical Review LettersNov 3, 199726 citations

Coexistence of superconductivity and density wave orders in a one-dimensional correlated system

Yan Xu, Weiting Chen, Hanqin Ding

Chinese Journal of PhysicsJul 24, 20202 citations

Charge-density-wave and pairing susceptibilities in a two-dimensional electron-phonon model

R. M. Noack, Douglas J. Scalapino, Richard T. Scalettar

We present quantum Monte Carlo results for a two-dimensional electron-phonon model. At half filling, a Peierls--charge-density-wave (CDW) instability dominates the behavior of the system and suppresses superconductivity. The CDW structure factor scales with system size and is consistent with a finite-size Ising-like scaling analysis which we use to estimate ${\mathit{T}}_{\mathit{c}}$ for the Peierls-CDW transition. Away from half filling, the Monte Carlo calculations show superconducting pairing in an s-wave channel, with a peak in the pair field susceptibility near a region in which there are strong Peierls-CDW correlations.We present quantum Monte Carlo results for a two-dimensional electron-phonon model. At half filling, a Peierls--charge-density-wave (CDW) instability dominates the behavior of the system and suppresses superconductivity. The CDW structure factor scales with system size and is consistent with a finite-size Ising-like scaling analysis which we use to estimate ${\mathit{T}}_{\mathit{c}}$ for the Peierls-CDW transition. Away from half filling, the Monte Carlo calculations show superconducting pairing in an s-wave channel, with a peak in the pair field susceptibility near a region in which there are strong Peierls-CDW correlations.

Physical Review LettersFeb 11, 1991106 citations

Strongly Correlated Electrons in Two Dimensions

S. V. Kravchenko

May 25, 201715 citations

A "negative" route to pair density wave order

Wang, Hao-Xin, Hu, Yi-Jian, Huang, Wen +1 more

Pair density waves (PDW) are novel forms of superconducting states that exhibit periodically modulated pairing. A remaining challenge is to elucidate how intrinsic PDW order can emerge robustly in strongly correlated electrons. Here we propose that PDW is prone to form in strongly coupled multiband superconductors simply with interband Cooper pairing between electrons from oppositely dispersing bands. This scenario is heuristically motivated by the observation that uniform interband pairing in such systems would exhibit negative superfluid weight -- a signature of an instability towards pairing modulation, implying that PDW emerges naturally in the true ground state. Using large-scale density-matrix-renormalization-group calculations with finite-size scaling analysis, we demonstrate this PDW mechanism in a minimal model with strong interband attractions. Our simulations reveal power-law superconducting correlations characterized by incommensurate modulations. The exponent $K_{sc}$ of the power-law PDW correlation decreases systematically with increasing ladder width, confirming a genuine long-range PDW order in the 2D limit. Our study therefore demonstrates a promising route to robust PDW states in multiband systems.Pair density waves (PDW) are novel forms of superconducting states that exhibit periodically modulated pairing. A remaining challenge is to elucidate how intrinsic PDW order can emerge robustly in strongly correlated electrons. Here we propose that PDW is prone to form in strongly coupled multiband superconductors simply with interband Cooper pairing between electrons from oppositely dispersing bands. This scenario is heuristically motivated by the observation that uniform interband pairing in such systems would exhibit negative superfluid weight -- a signature of an instability towards pairing modulation, implying that PDW emerges naturally in the true ground state. Using large-scale density-matrix-renormalization-group calculations with finite-size scaling analysis, we demonstrate this PDW mechanism in a minimal model with strong interband attractions. Our simulations reveal power-law superconducting correlations characterized by incommensurate modulations. The exponent $K_{sc}$ of the power-law PDW correlation decreases systematically with increasing ladder width, confirming a genuine long-range PDW order in the 2D limit. Our study therefore demonstrates a promising route to robust PDW states in multiband systems.

arXiv:2512.06100Dec 5, 20250 citations

Strongly Correlated Electrons in Two Dimensions

Pan Stanford Publishing Pte. Ltd. eBooksNov 30, 20166 citations

{\mathit{T}}_{\mathit{c}}

for the Peierls-CDW transition. Away from half filling, the Monte Carlo calculations show superconducting pairing in an s-wave channel, with a peak in the pair field susceptibility near a region in which there are strong Peierls-CDW correlations.

K_{sc}

of the power-law PDW correlation decreases systematically with increasing ladder width, confirming a genuine long-range PDW order in the 2D limit. Our study therefore demonstrates a promising route to robust PDW states in multiband systems.