The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations

Abstract

We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function -- \textit{waterfall} features and narrow spin-polaron bands -- is only visible in the lattice QMC approach.

arXiv comment10 pages + appendix on the structure of the self energy; 5 figures

References in corpus (53)

• The electronic properties of graphene
• Correlated Electrons in High Temperature Superconductors
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Emergence of magnetism in graphene materials and nanostructures
• A continuous-time solver for quantum impurity models
• Magnetism in graphene nano-islands
• Functional renormalization group approach to correlated fermion systems
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Pseudogap induced by short-range spin correlations in a doped Mott insulator
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Relativistic Mott criticality in graphene
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Quasiparticle Dispersion of the 2D Hubbard Model: From an Insulator to a Metal
• Spatial Correlations in Dynamical Mean Field Theory
• Dynamical Signatures of Edge-State Magnetism on Graphene Nanoribbons
• Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Pseudogaps and their Interplay with Magnetic Excitations in the doped 2D Hubbard Model
• Doped high-Tc cuprate superconductors elucidated in the light of zeros and poles of electronic Green's function
• Single hole dynamics in the t-J model on a square lattice
• Edge State Magnetism of Single Layer Graphene Nanostructures
• High energy kink in the single particle spectra of the two-dimensional Hubbard model
• Quantum Phase Transitions of a Square-Lattice Heisenberg Antiferromagnet with Two Kinds of Nearest-Neighbour Bonds: A High-Order Coupled-Cluster Treatment
• Identifying the maximum entropy method as a special limit of stochastic analytic continuation
• Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
• The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code
• Site dilution of quantum spins in the honeycomb lattice
• Dynamical structure factors and excitation modes of the bilayer Heisenberg model
• Unified quantitative model for magnetic and electronic spectra of the undoped cuprates
• Momentum-dependent pseudogaps in the half-filled two-dimensional Hubbard model
• Absence of spin liquid in non-frustrated correlated systems
• Magnetism in strained graphene dots
• Phase diagram and Fermi-liquid properties of the extended Hubbard model on the honeycomb lattice
• Dynamical Mean Field Study of The Dirac Liquid
• Temperature and doping dependence of high-energy kink in cuprates
• Spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping
• Finite temperature semimetal-insulator transition on the honeycomb lattice
• Spectral function of the 2D Hubbard model: a density matrix renormalization group plus cluster perturbation theory study
• Zero-modes and global antiferromagnetism in strained graphene
• Effective magnetic correlations in hole-doped graphene nanoflakes
• Cluster dynamical mean field theory of quantum phases on a honeycomb lattice
• Universal waterfalls-like feature in the spectral function of high temperature superconductors
• Coulomb correlations in the honeycomb lattice: role of translation symmetry
• Multiband Dual Fermion Approach to Quantum Criticality in the Hubbard Honeycomb Lattice
• Spin-polaron band structure and hole pockets in underdoped cuprates
• Interplay between the edge-state magnetism and long-range Coulomb interaction in zigzag graphene nanoribbons: quantum Monte Carlo study
• Influence of Magnetism and Correlation on the Spectral Properties of Doped Mott Insulators

Cited by in corpus (35)

• Quantum Critical Points and the Sign Problem
• Quantum phase transitions in Dirac fermion systems
• Doping-induced quantum spin Hall insulator to superconductor transition
• A perspective on machine learning and data science for strongly correlated electron problems
• Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
• Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations
• Learning quantum phase transitions through Topological Data Analysis
• Deconfinement of Mott Localized Electrons into Topological and Spin-Orbit Coupled Dirac Fermions
• Spin-caloritronic transport in hexagonal graphene nanoflakes
• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
• Edge magnetic properties of black phosphorene nanoribbons
• Stripe order in the doped Hubbard model on the honeycomb lattice
• Low-depth simulations of fermionic systems on square-grid quantum hardware
• Doping fingerprints of spin and lattice fluctuations in moiré superlattice systems
• Exact and many-body perturbation solutions of the Hubbard model applied to linear chains
• Phase diagram of the Hubbard model on a honeycomb lattice: A cluster slave-spin study
• Local moments versus itinerant antiferromagnetism: magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model
• Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Next-generation EDIpack: A Lanczos-based package for quantum impurity models featuring general broken-symmetry phases, flexible bath topologies and multi-platform interoperability
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions
• Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene
• The Fractal-Lattice Hubbard Model
• Instanton gas approach to the Hubbard model
• The odd-parity altermagnetism: A spin group study
• Effect of electronic correlation on topological end-states in finite-size graphene nanoribbons
• Mean-field approximation of the Hubbard model expressed in a many-body basis
• Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
• Robust correlated magnetic moments in end-modified graphene nanoribbons
• Modulated honeycomb lattices and their magnetic properties
• Magnetism of magic-angle twisted bilayer graphene
• Electronic and magnetic properties of honeycomb zigzag nanoribbons in the in-plane transverse electric field using Kane-Mele-Hubbard model
• Hubbard Model on the Honeycomb Lattice with an Indefinite Long-Range Interaction