Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models

Abstract

In a general class of one and two dimensional Hubbard models, we prove upper bounds for the two-point correlation functions at finite temperatures for electrons, for electron pairs, and for spins. The upper bounds decay exponentially in one dimension, and with power laws in two dimensions. The bounds rule out the possibility of the corresponding condensation of superconducting electron pairs, and of the corresponding magnetic ordering. Our method is general enough to cover other models such as the t-J model.

LaTeX, 8 pages, no figures. A reference appeared after the publication is added

Cited by in corpus (30)

• Spectral Gap and Exponential Decay of Correlations
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• d- and p-wave superconductivity mediated by spin fluctuations in two- and three-dimensional single-band repulsive Hubbard model
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Electron-phonon interaction and transport properties of metallic bulk and monolayer transition metal dichalcogenide TaS${}_2$
• Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence
• Random loop representations for quantum spin systems
• Some Properties of Correlations of Quantum Lattice Systems in Thermal Equilibrium
• Does the Hubbard Model Show $d_{x^2-y^2}$ Superconductivity?
• Ferromagnetism beyond Lieb's theorem
• First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction
• Strongly correlated superconductivity with long-range spatial fluctuations
• Classical XY Model in 1.99 Dimensions
• Phase separation and electron pairing in repulsive Hubbard clusters
• Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities
• Production of minimally entangled typical thermal states with the Krylov-space approach
• Decay of correlations in 2D quantum systems with continuous symmetry
• Exponential decay of correlation functions in many-electron systems
• Does the 2D Hubbard Model Really Show d-Wave Superconductivity?
• Superconductivity in the Extended Hubbard Model with More Than Nearest-Neighbour Contributions
• Spectral Gap and Decay of Correlations in U(1)-Symmetric Lattice Systems in Dimensions D<2
• Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases
• Bound states in the phase diagram of the extended Hubbard model
• Bogolyubov inequality for the ground state and its application to interacting rotor systems
• A rigorous treatment of the perturbation theory for many-electron systems
• Decay of Superconducting Correlations for Gauged Electrons in Dimensions $D\le 4$
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches
• Ground-state correlations of itinerant electrons in the spinless Falicov-Kimball chain and related tight-binding systems
• Quantum Vorticity at positive temperature for spin systems with continuous symmetry
• Magnetization of electronic ground states in frustrated superstable graphs