Composite fermion-boson mapping for fermionic lattice models

Abstract

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the one- and two-dimensional Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.

References in corpus (15)

• The density-matrix renormalization group
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Wave function optimization in the variational Monte Carlo method
• Plaquette Boson-Fermion Model of Cuprates
• Pairing Correlations in the Two-Dimensional Hubbard Model
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Mott physics and first-order transition between two metals in the normal state phase diagram of the two-dimensional Hubbard model
• Mott transition in one dimension: Benchmarking dynamical cluster approaches
• Exact Transformation for Spin-Charge Separation of Spin-half Fermions without Constraints
• Composite Boson Mapping for Lattice Boson Systems
• Correlated Wave-Functions and the Absence of Long Range Order in Numerical Studies of the Hubbard Model
• Nonlinear Bogolyubov-Valatin transformations: 2 modes
• U(1) slave-particle study of the finite-temperature doped Hubbard model in one and two dimensions

Cited by in corpus (3)

• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• Cluster Gutzwiller study of Bose-Hubbard ladder: ground-state phase diagram and many-body Landau-Zener dynamics