The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature

Abstract

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a novel connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at unprecedentedly low temperatures $T\ge 0.067$ for interactions up to $U\le 8$, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.

References in corpus (78)

• Cold bosonic atoms in optical lattices
• Complexity in Strongly Correlated Electronic Systems
• Quantum computational chemistry
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• A Mott insulator of fermionic atoms in an optical lattice
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Progress and perspectives on the electron-doped cuprates
• Continuous Time Quantum Monte Carlo method for fermions
• Quantum Magnetic Excitations from Stripes in Copper-Oxide Superconductors
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• The Hubbard model: A computational perspective
• Spatially modulated "Mottness" in La2-xBaxCuO4
• Resonant x-ray scattering studies of charge order in cuprates
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Site-resolved measurement of the spin-correlation function in the Hubbard model
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Superconductivity and the Pseudogap in the two-dimensional Hubbard model
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Stripe order, depinning, and fluctuations in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$ and La${}_{1.875}$Ba${}_{0.075}$Sr${}_{0.050}$CuO${}_4$
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Feynman diagrams versus Fermi-gas Feynman emulator
• Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors
• Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices
• Momentum space anisotropy and pseudogaps: a comparative cluster dynamical mean field analysis of the doping-driven metal-insulator transition in the two dimensional Hubbard model
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Fate of the false Mott-Hubbard transition in two dimensions
• Diagrammatic Monte Carlo
• Diagrammatic Monte Carlo for Correlated Fermions
• Stripe order from the perspective of the Hubbard model
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Commensurate spin dynamics in the superconducting state of an electron-doped cuprate superconductor
• Stripes on a 6-Leg Hubbard Ladder
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Critical temperature for the two-dimensional attractive Hubbard Model
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
• One-dimensional metallic behavior of the stripe phase in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices
• Formation and dynamics of anti-ferromagnetic correlations in tunable optical lattices
• Doping-driven Mott transition in the one-band Hubbard model
• Phase separation in the Hubbard model
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model
• Phase separation and competition of superconductivity and magnetism in the two-dimensional Hubbard model: From strong to weak coupling
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Interaction-Induced Adiabatic Cooling for Antiferromagnetism in Optical Lattices
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Quantum criticality with a twist - interplay of correlations and Kohn anomalies in three dimensions
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• Diagrammatic Monte Carlo for Dual Fermions
• Dynamics of Kondo voltage splitting after a quantum quench
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Incommensurate nematic fluctuations in two dimensional metals
• Spin-stripe density varies linearly with hole content in single-layer Bi2201 cuprate
• Spin Density Waves in the Hubbard model - A DMFT approach
• Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model
• Stability of Dirac Liquids with Strong Coulomb Interaction
• Atomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity
• Real-frequency Diagrammatic Monte Carlo at Finite Temperature
• A dynamical mean-field theory study of stripe order and d-wave superconductivity in the two-dimensional Hubbard model
• Phase diagram topology of the Haldane-Hubbard-Coulomb model
• Renormalized perturbation theory at large expansion orders
• Diagrammatic Monte Carlo algorithm for the resonant Fermi gas
• Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model
• Slave-Boson analysis of the 2D Hubbard model
• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Entropy in the non-Fermi-liquid regime of the doped $2d$ Hubbard model
• Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model
• Dynamically enhanced magnetic incommensurability: Effects of local dynamics on non-local spin-correlations in a strongly correlated metal
• Superfluid ground state phase diagram of the two-dimensional Hubbard model in the emergent Bardeen-Cooper-Schrieffer regime
• Strong-coupling diagrammatic Monte Carlo technique for correlated fermions and frustrated spins
• Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory
• The phase diagram of the Hubbard model by Variational Auxiliary Field quantum Monte Carlo

Cited by in corpus (3)

• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• Magnetic properties and pseudogap formation in infinite-layer nickelates: insights from the single-band Hubbard model
• Spectral shift technique for strongly correlated lattice fermions