Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

Abstract

By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping $t$, the on-site electron-electron interaction $U$, the phonon energy ${\omega }_0$, and the electron-phonon coupling $g$. At half filling, the ground state is an antiferromagnetic insulator for $U\gtrsim 2g^2/{\omega }_0$, while it is a charge-density-wave (or bi-polaronic) insulator for $U\lesssim 2g^2/{\omega }_0$. In addition to these phases, we find a superconducting phase that intrudes between them. For ${\omega }_0/t=1$, superconductivity emerges when both $U/t$ and $2g^2/t{\omega }_0$ are small; then, by increasing the value of the phonon energy ${\omega }_0$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.

11 pages, 10 figures

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• Electron-phonon Interaction close to a Mott transition
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• Metal-insulator transition in the one-dimensional Holstein model at half filling
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• Electron-phonon vertex in the two-dimensional one-band Hubbard model
• Competition between antiferromagnetic and charge density wave order in the half filled Hubbard-Holstein model
• Metallicity in the half-filled Holstein-Hubbard model
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• Phase separation in the Hubbard model
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• Effect of electron correlation on phonons in a strongly-coupled electron-phonon system
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• TurboRVB: a many-body toolkit for {\it ab initio} electronic simulations by quantum Monte Carlo
• Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
• Strong Coupling Limit of the Holstein-Hubbard Model
• Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study
• Langevin Simulations of a Long Range Electron Phonon Model
• Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene
• Superconductivity, Charge-Density-Waves, and Bipolarons in the Holstein model
• Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice
• Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Solution of the "sign problem" for the half filled Hubbard-Holstein model
• Stripe correlations in the two-dimensional Hubbard-Holstein model
• Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
• Magnetism and charge order in the honeycomb lattice
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Fluctuating Nature of Light-Enhanced $d$-Wave Superconductivity: A Time-Dependent Variational Non-Gaussian Exact Diagonalization Study
• Charge Density Wave and Superconductivity in the Disordered Holstein Model
• Variational wave functions for the spin-Peierls transition in the Su-Schrieffer-Heeger model with quantum phonons
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Phonon-induced pairing in quantum dot quantum simulator
• Machine learning the relationship between Debye temperature and superconducting transition temperature
• Study of the superconducting order parameter in the negative-$U$ 2D-Hubbard model by grand-canonical twist-averaged boundary conditions
• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Real-time evolution of static electron-phonon models in time-dependent electric fields
• Competing Correlated Insulators in multi-orbital systems coupled to phonons
• Theory of electron-phonon interactions in extended correlated systems probed by resonant inelastic x-ray scattering
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Role of Matter Interactions in Superradiant Phenomena
• Charge correlations suppress unconventional pairing in the Holstein model
• Antiferromagnetic and bond-order-wave phases in the half-filled two-dimensional optical Su-Schrieffer-Heeger-Hubbard model
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study
• Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of $s$-wave pairing between charge and magnetic orders
• Probing the pseudogap and beyond: Examining single-particle properties of the hole- and electron-doped Hubbard model
• Insulating and metallic phases in the one-dimensional Hubbard-Su-Schrieffer-Heeger model: Insights from a backflow-inspired variational wave function