Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study

Abstract

The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two dimensional Holstein model are computed using determinant quantum Monte Carlo (DQMC), and compared with results computed using the Migdal-Eliashberg (ME) approach. We access temperatures as low as 25 times less than the Fermi energy, $E_F$, which are still above the SC transition. We find that the SC susceptibility at low $T$ agrees quantitatively with the ME theory up to a dimensionless electron-phonon coupling ${\lambda }_0\approx 0.4$ but deviates dramatically for larger ${\lambda }_0$. We find that for large ${\lambda }_0$ and small phonon frequency ${\omega }_0\ll E_F$ CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.

7 pages, 7 figures. v2: discussion improved, added supplemental material

References in corpus (1)

• Electron and phonon dispersions of the two dimensional Holstein model: Effects of vertex and non-local corrections

Cited by in corpus (89)

• Planckian Dissipation in Metals
• Eliashberg Theory: a short review
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Nonstandard superconductivity or no superconductivity in hydrides under high pressure
• Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
• Bipolaronic high-temperature superconductivity
• Phonon dispersion and the competition between pairing and charge order
• Superconductivity and charge density wave order in the 2D Holstein model
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• A bound on superconducting $T_c$'s
• Antiferromagnetism induced by electron-phonon-coupling
• Pseudogap crossover in the electron-phonon system
• Paramagnons and high-temperature superconductivity in mercury-based cuprates
• Competition of electron-phonon mediated superconductivity and Stoner magnetism on a flat band
• Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques
• Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation
• Heuristic bounds on superconductivity and how to exceed them
• Future Study of Dense Superconducting Hydrides at High Pressure
• Superconductivity, Charge-Density-Waves, and Bipolarons in the Holstein model
• Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
• Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity
• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Langevin Simulations of the Half-Filled Cubic Holstein Model
• A perspective on machine learning and data science for strongly correlated electron problems
• A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in BaBiO${}_3$
• Superconductivity in the presence of strong electron-phonon interactions and frustrated charge order
• The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids
• Progress, problems and prospects of room-temperature superconductivity
• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• Migdal-Eliashberg theory as a classical spin chain
• Electronic and phononic properties of a two dimensional electron gas coupled to dipolar phonons via small-momentum-transfer scattering
• A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model
• Free energy and specific heat near a quantum critical point of a metal
• A stability bound on the $T$-linear resistivity of conventional metals
• Charge Density Wave and Superconductivity in the Disordered Holstein Model
• Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons
• Bipolaronic superconductivity out of a Coulomb gas
• Charge order in the kagome lattice Holstein model: A hybrid Monte Carlo study
• Mitigating the fermion sign problem by automatic differentiation
• Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems
• Quantum Monte Carlo study of an anharmonic Holstein model
• Towards exact solutions for the superconducting $T_c$ induced by electron-phonon interaction
• "Quantum bipolaron" superconductivity from quadratic electron-phonon coupling
• The pairing glue in cuprate superconductors from the self-energy revealed via machine learning
• Planckian relaxation delusion in metals
• Limits of Eliashberg Theory and Bounds for Superconducting Transition Temperature
• Enhancement of superconductivity with external phonon squeezing
• Electron - phonon coupling in Eliashberg - McMillan theory beyond adiabatic approximation
• Robust Fermi liquid instabilities in sign problem-free models
• Machine learning the relationship between Debye temperature and superconducting transition temperature
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Moire superconductivity
• Antiadiabatic Phonons and Superconductivity in Eliashberg-McMillan Theory
• Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory
• Electron-phonon coupling and superconductivity in the doped topological-crystalline insulator (Pb${}_{0.5}$Sn${}_{0.5}$)${}_{1-x}$In${}_x$Te
• Semi-classical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model
• Instability of metals with respect to strong electron-phonon interaction
• Nonperturbative self-consistent electron-phonon spectral functions and transport
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. I: The $\gamma$-model
• Superconductor discovery in the emerging paradigm of Materials Informatics
• Universal scaling relations in electron-phonon superconductors
• Electron-phonon vertex correction effect in superconducting H3S
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model
• High-temperature superconductivity induced by the Su-Schrieffer-Heeger electron-phonon coupling
• Collective modes in the charge-density wave state of K${}_{0.3}$MoO${}_3$: The role of long-range Coulomb interactions revisited
• Phonon renormalization and Pomeranchuk instability in the Holstein model
• Strong electron-phonon coupling and phonon-induced superconductivity in tetragonal C${}_3$N${}_4$ with hole doping
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. III: Einstein phonons
• Charge correlations suppress unconventional pairing in the Holstein model
• Identifying materials with charge-spin physics using charge-spin susceptibility computed from first principles
• High-Temperature Superconductivity from Finite-Range Attractive Interaction
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. II: Dispersive phonons
• Charge-Density-Wave State in Extremely Overdoped Cuprates Driven by Phonons
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• The influence of phonon symmetry and electronic structure on the electron-phonon coupling momentum dependence in cuprates
• Dynamical Approach to Realize Room-Temperature Superconductivity in LaH${}_{10}$
• Spectral signatures of residual electron pairing in the extended-Hubbard-Su-Schrieffer-Heeger model
• Possibilities for enhanced electron-phonon interactions and high-$T_c$ superconductivity in engineered bimetallic nano-structured superlattices
• Doping dependence and multichannel mediators of superconductivity: Calculations for a cuprate model
• Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• Ward identity preserving approach for investigation of phonon spectrum with self-energy and vertex corrections
• Superconductivity near an Ising nematic quantum critical point in two dimensions
• Disorder Suppression of Charge Density Waves in the Honeycomb Holstein Model
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings
• Commensurate to Incommensurate Transition of Three Dimensional Charge Density Waves
• Upper bound on $T_c$ in a strongly coupled electron-boson superconductor