Phase diagram of the Hubbard model on a square lattice: A cluster slave-spin study

Abstract

We employ the cluster slave-spin method to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\delta$ and coupling strength $U$ being its parameters. In addition to a crossover reflected in the behavior of the antiferromagnetic gap ${\Delta }_{\text{AFM}}$, this property can also be observed in the energetics of the cluster slave-spin Hamiltonian -- the antiferromagnetism at small $U$ is due to the potential energy gain while that in the strong coupling limit is driven by the kinetic energy gain, which is consistent with the results from the cluster dynamical mean-field theory calculation and the quantum Monte Carlo simulation. We find the interaction $U_c$ for the crossover in the AFM state, separating the weak- and strong- coupling regimes, almost remains unchanged upon doping, and it is smaller than the critical coupling strength $U_{\text{Mott}}$ for the first-order metal-insulator Mott transition in the half-filled paramagnetic state. At half-filling, a relationship between the staggered magnetization $M$ and ${\Delta }_{\text{AFM}}$ is established in the small $U$ limit to nullify the Hartree-Fock theory, and a first-order Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at $U_{\text{Mott}}=10t$. Finally, an overall phase diagram in the $U$-$\delta$ plane is presented, which is composed of four regimes: the antiferromagnetic insulator, the antiferromagnetic metal with the compressibility $\kappa >0$ or $\kappa <0$, and the paramagnetic metal, as well as three phase transitions: (i) From the antiferromagnetic metal to the paramagnetic metal, (ii) between the antiferromagnetic metal phases with positive and negative $\kappa$, and (iii) separating the antiferromagnetic insulating phase from the antiferromagnetic metal phase.

Accepted for publication as a Regular Article in Physical Review B

References in corpus (13)

• Cluster Dynamical Mean Field Theory of the Mott Transition
• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Fate of the false Mott-Hubbard transition in two dimensions
• Rotationally-invariant slave-boson formalism and momentum dependence of the quasiparticle weight
• U(1) Slave-spin theory and its application to Mott transition in a multi-orbital model for iron pnictides
• Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
• Self-consistent slave rotor mean field theory for strongly correlated systems
• Hidden Mott transition and large-$U$ superconductivity in the two-dimensional Hubbard model
• Kinetic-energy driven superconductivity in cuprate superconductors
• Precise Determination of Phase Diagram for Two-Dimensional Hubbard Model with Filling- and Bandwidth-Control Mott Transitions: Grand-Canonical Path-Integral Renormalization Group Approach
• Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model
• Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model
• Revisit of Antiferromagnetism in Hubbard Model by A Cluster Slave-Spin Method

Cited by in corpus (3)

• Phase diagram of the Hubbard model on a honeycomb lattice: A cluster slave-spin study
• The odd-parity altermagnetism: A spin group study
• Evolution of magnetic correlation in an inhomogeneous square lattice