Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions

Abstract

We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density wave for $U<-4V$ and $V>0$, s-wave superconductivity for $U<0$ and small negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.

11 pages, 11 figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Abundance of correlated insulating states at fractional fillings of WSe${}_2$/WS${}_2$ moiré superlattices
• The Hubbard Model
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Anomalously Strong Near-Neighbor Attraction in Doped 1D Cuprate Chains
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates
• Phase diagram of the Kane-Mele-Coulomb model
• Charge order and antiferromagnetism in the extended Hubbard model
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Enhancing $d$-wave superconductivity with nearest-neighbor attraction of extended Hubbard model
• Thermodynamics of the metal-insulator transition in the extended Hubbard model
• Superlight pairs in face-centred-cubic extended Hubbard models with strong Coulomb repulsion

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