Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice

Abstract

We study spinless fermions with nearest-neighbor repulsive interactions ($t$-$V$ model) on the two-dimensional three-band Lieb lattice. At half-filling, the free electronic band structure consists of a flat band at zero energy and a single cone with linear dispersion. The flat band is expected to be unstable upon inclusion of electronic correlations, and a natural channel is charge order. However, due to the three-orbital unit cell, commensurate charge order implies an imbalance of electron and hole densities and therefore doping away from half-filling. Our numerical results show that below a finite-temperature Ising transition a charge density wave with one electron and two holes per unit cell and its partner under particle-hole transformation are spontaneously generated. Our calculations are based on recent advances in auxiliary-field and continuous-time quantum Monte Carlo simulations that allow sign-free simulations of spinless fermions at half-filling. It is argued that particle-hole symmetry breaking provides a route to access levels of finite doping, without introducing a sign problem.

arXiv comment9 pages, 6 figures, added data for strong Coulomb repulsion and classical Ising-limit

References in corpus (42)

• Continuous-time Monte Carlo methods for quantum impurity models
• Room temperature magnetic order on zigzag edges of narrow graphene nanoribbons
• Observation of a localized flat-band state in a photonic Lieb lattice
• Continuous Time Quantum Monte Carlo method for fermions
• Observation of bound states in Lieb photonic lattices
• High-temperature surface superconductivity in topological flat-band systems
• Geometric origin of superfluidity in the Lieb lattice flat band
• Topological Insulators on the Lieb and Perovskite Lattices
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
• Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices
• 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
• Diagrammatic Determinantal methods: projective schemes and applications to the Hubbard-Holstein model
• Superconducting Transitions in Flat Band Systems
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Spectral and transport properties of the two-dimensional Lieb lattice
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Solution to sign problems in half-filled spin-polarized electronic systems
• A quantum Monte-Carlo method for fermions, free of discretization errors
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• A simple fermionic model of deconfined phases and phase transitions
• Phase diagram of the Kane-Mele-Coulomb model
• Infinite Variance in Fermion Quantum Monte Carlo Calculations
• Quantum Simulation of a Topological Mott Insulator with Rydberg Atoms in a Lieb Lattice
• Edge-Ferromagnetism from Majorana Flat-Bands: Application to Split Tunneling-Conductance Peaks in the High-Tc Cuprates
• Instabilities at [110] Surfaces of d_{x^2-y^2} Superconductors
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Ferromagnetism beyond Lieb's theorem
• Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
• Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities
• Zero-modes and global antiferromagnetism in strained graphene
• Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice
• Spontaneous time-reversal symmetry breaking in the boundary Majorana flat bands
• Ground State Degeneracy of Interacting Spinless Fermions
• The relationship between Hirsch-Fye and weak coupling diagrammatic Quantum Monte Carlo methods
• Edge instabilities of topological superconductors
• Coexistence of s-wave Superconductivity and Antiferromagnetism

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• Strain induced superconductor-insulator transition on Lieb lattice
• Kondo Breakdown via Fractionalization in a Frustrated Kondo Lattice Model
• Quantum Anomalous Hall Phase Stabilized via Realistic Interactions on a Kagome Lattice
• Mitigating the fermion sign problem by automatic differentiation
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Dynamical resilience to disorder: the dilute Hubbard model on the Lieb lattice
• 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
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