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:2503.12463 · Physical review. B./Physical review. B

Entanglement in the pseudogap regime of cuprate superconductors

Frederic Bippus, Juraj Krsnik, Motoharu Kitatani, Luka Akšamović, Anna Kauch, N. Barišić, Karsten Held

Published Jul 30, 2025• 4 citations
arXivHTMLPDF

Abstract

We find a strongly enhanced entanglement within the pseudogap regime of the Hubbard model. This entanglement is estimated from the quantum Fisher information and, avoiding the ill-conditioned analytical continuation, the quantum variance. Both are lower bounds for the actual entanglement and can be calculated from the (antiferromagnetic) susceptibility, obtained here with the dynamical vertex approximation. Our results qualitatively agree with experimental neutron scattering experiments for various cuprates. Theory predicts a ln ( 1 / T ) divergence of the entanglement for low temperatures T , which is however cut off by the onset of superconductivity.

DOI
10.1103/xk42-b9cx

Related papers

Pseudogap Induced by Antiferromagnetic Spin Correlation in High-Temperature Superconductors

Tôru Sakai, Yoshinori Takahashi

The pseudogap phenomena observed on cuprate high temperature superconductors are investigated based on the exact diagonalization method on the finite cluster t-J model. The results show the presence of the gap-like behavior in the temperature dependence of various magnetic properties; the NMR relaxation rate, the neutron scattering intensity and the static susceptibility. The calculated spin correlation function indicates that the pseudogap behavior arises associated with the development of the antiferromagnetic spin correlation with decreasing the temperature. The numerical results are presented to clarify the model parameter dependence, that covers the realistic experimental situation. The effect of the next-nearest neighbor hopping $t'$ is also studied.

arXiv:cond-mat/0010448•Journal of the Physical Society of Japan•Jan 15, 2001•14 citations

Pseudogap and Spin Fluctuations in the Normal State of the Electron-Doped Cuprates

Bumsoo Kyung, V. Hankevych, A.-M. Daré +1 more

We present reliable many-body calculations for the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature-dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering, and for the phase diagram.

arXiv:cond-mat/0312499•Physical Review Letters•Sep 29, 2004•124 citations

Rise and fall of the pseudogap in the Emery model, insights for cuprates

M. O. Malcolms, Henri Menke, Yi-Ting Tseng +4 more

Abstract The pseudogap in high-temperature superconducting cuprates is an exotic state of matter, displaying emerging Fermi arcs and a momentum-selective suppression of spectral weight upon cooling. We show how these phenomena are captured in the three-band Emery model by performing dynamical vertex approximation calculations for its normal state. For the hole-doped parent compound, our results demonstrate the formation of a pseudogap due to short-ranged commensurate antiferromagnetic fluctuations. At larger doping values, progressively, incommensurate correlations and a metallic regime appear. Our results are in qualitative agreement with this doping trend in the normal state of cuprates, and hence, represent a step towards the uniform description of their phase diagrams within a single theoretical framework.

arXiv:2412.14951•Communications Physics•May 19, 2026•2 citations

Theory of Antiferromagnetic Correlations in High-Tc Cuprates

Masatoshi Imada

A phenomenological theory of the antiferromagnetic correlations in cuprates is constructed from analyses of recent numerical results of the Hubbard model. Two crossover temperatures are predicted to exist. In three regions divided by the two crossover temperatures, we present a qualitative but explicit form of doping and temperature dependences of the dynamical susceptibility χ( q , ω), which agrees with NMR and neutron scattering data of cuprates. It solves recent controversy between these two experimental results and provides us with a unified picture of antiferromagnetic correlation in cuprates.

Journal of the Physical Society of Japan•Mar 15, 1994•17 citations

Emergence of spin entanglement with the pseudogap onset in the Fermi-Hubbard model

Frederic Bippus, Thomas Chalopin, Gabriele Bellomia +6 more

Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.

cond-mat.str-elCross-listedarXiv:2605.31240•Jun 1, 2026•0 citations

Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards a quantitative theory (Review Article)

A.–M. S. Tremblay, Bumsoo Kyung, David Sénéchal

This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole- and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the two-particle self-consistent approach, variational cluster perturbation theory (or variational cluster approximation), and cellular dynamical mean-field theory.

arXiv:cond-mat/0511334•Low Temperature Physics•Apr 1, 2006•194 citations
We find a strongly enhanced entanglement within the pseudogap regime of the Hubbard model. This entanglement is estimated from the quantum Fisher information and, avoiding the ill-conditioned analytical continuation, the quantum variance. Both are lower bounds for the actual entanglement and can be calculated from the (antiferromagnetic) susceptibility, obtained here with the dynamical vertex approximation. Our results qualitatively agree with experimental neutron scattering experiments for various cuprates. Theory predicts a ln ( 1 / T ) divergence of the entanglement for low temperatures T , which is however cut off by the onset of superconductivity.
The pseudogap phenomena observed on cuprate high temperature superconductors are investigated based on the exact diagonalization method on the finite cluster t-J model. The results show the presence of the gap-like behavior in the temperature dependence of various magnetic properties; the NMR relaxation rate, the neutron scattering intensity and the static susceptibility. The calculated spin correlation function indicates that the pseudogap behavior arises associated with the development of the antiferromagnetic spin correlation with decreasing the temperature. The numerical results are presented to clarify the model parameter dependence, that covers the realistic experimental situation. The effect of the next-nearest neighbor hopping t′t't′ is also studied.
We present reliable many-body calculations for the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature-dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering, and for the phase diagram.
Abstract The pseudogap in high-temperature superconducting cuprates is an exotic state of matter, displaying emerging Fermi arcs and a momentum-selective suppression of spectral weight upon cooling. We show how these phenomena are captured in the three-band Emery model by performing dynamical vertex approximation calculations for its normal state. For the hole-doped parent compound, our results demonstrate the formation of a pseudogap due to short-ranged commensurate antiferromagnetic fluctuations. At larger doping values, progressively, incommensurate correlations and a metallic regime appear. Our results are in qualitative agreement with this doping trend in the normal state of cuprates, and hence, represent a step towards the uniform description of their phase diagrams within a single theoretical framework.
A phenomenological theory of the antiferromagnetic correlations in cuprates is constructed from analyses of recent numerical results of the Hubbard model. Two crossover temperatures are predicted to exist. In three regions divided by the two crossover temperatures, we present a qualitative but explicit form of doping and temperature dependences of the dynamical susceptibility χ( q , ω), which agrees with NMR and neutron scattering data of cuprates. It solves recent controversy between these two experimental results and provides us with a unified picture of antiferromagnetic correlation in cuprates.
Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.
This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole- and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the two-particle self-consistent approach, variational cluster perturbation theory (or variational cluster approximation), and cellular dynamical mean-field theory.