Composite particle mapping for boson and fermion lattice systems

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster 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 1D and 2D 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.We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster 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 1D and 2D 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.

arXiv:1408.1014Journal of Physics Condensed MatterOct 16, 20143 citations

Jordan-Wigner composite fermion liquids in a two-dimensional quantum spin ice

Leonardo Goller, Inti Sodemann

The Jordan-Wigner map in two dimensions is an exact lattice regularization of the $2\ensuremath{\pi}$-flux attachment to a hard-core boson (or spin $\frac{1}{2}$ ) leading to a composite fermion particle. When the spin- $\frac{1}{2}$ model obeys ice rules this map preserves locality, namely, local Rohkshar-Kivelson (RK) models of spins are mapped onto local models of Jordan-Wigner composite fermions. Using this composite fermion dual representation of RK models we construct spin-liquid states by projecting Slater determinants onto the subspaces of the ice rules. Interestingly, we find that these composite fermions behave as ``dipolar'' partons for which the projective implementations of symmetries are very different from standard ``pointlike'' partons. We construct interesting examples of these composite Fermi-liquid states that respect all microscopic symmetries of the RK model. In the six-vertex subspace, we constructed a time-reversal and particle-hole-invariant state featuring two massless Dirac nodes, which is a composite fermion counterpart to the classic $\ensuremath{\pi}$-flux state of Abrikosov fermions in the square lattice. This state is a good ground-state candidate for a modified RK--type Hamiltonian of quantum spin ice. In the dimer subspace, we constructed a state featuring a composite Fermi surface but with nesting instabilities towards ordered phases such as the columnar state. We have also analyzed the low-energy emergent gauge structure. If one ignores confinement, the system would feature a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ low-energy gauge structure with two associated gapless photon modes, but with the composite fermion carrying gauge charge only for one photon and behaving as a gauge-neutral dipole under the other. These states are also examples of pseudoscalar $\text{U}(1)$ spin liquids where mirror and time-reversal symmetries act as composite fermion particle-hole conjugations, and the emergent magnetic fields are even under such time-reversal or lattice mirror symmetries.The Jordan-Wigner map in two dimensions is an exact lattice regularization of the $2\ensuremath{\pi}$-flux attachment to a hard-core boson (or spin $\frac{1}{2}$) leading to a composite fermion particle. When the spin-$\frac{1}{2}$ model obeys ice rules this map preserves locality, namely, local Rohkshar-Kivelson (RK) models of spins are mapped onto local models of Jordan-Wigner composite fermions. Using this composite fermion dual representation of RK models we construct spin-liquid states by projecting Slater determinants onto the subspaces of the ice rules. Interestingly, we find that these composite fermions behave as ``dipolar'' partons for which the projective implementations of symmetries are very different from standard ``pointlike'' partons. We construct interesting examples of these composite Fermi-liquid states that respect all microscopic symmetries of the RK model. In the six-vertex subspace, we constructed a time-reversal and particle-hole-invariant state featuring two massless Dirac nodes, which is a composite fermion counterpart to the classic $\ensuremath{\pi}$-flux state of Abrikosov fermions in the square lattice. This state is a good ground-state candidate for a modified RK--type Hamiltonian of quantum spin ice. In the dimer subspace, we constructed a state featuring a composite Fermi surface but with nesting instabilities towards ordered phases such as the columnar state. We have also analyzed the low-energy emergent gauge structure. If one ignores confinement, the system would feature a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ low-energy gauge structure with two associated gapless photon modes, but with the composite fermion carrying gauge charge only for one photon and behaving as a gauge-neutral dipole under the other. These states are also examples of pseudoscalar $\text{U}(1)$ spin liquids where mirror and time-reversal symmetries act as composite fermion particle-hole conjugations, and the emergent magnetic fields are even under such time-reversal or lattice mirror symmetries.

arXiv:2309.13116Physical review. B./Physical review. BJan 26, 20241 citation

A test of boson mappings of fermion systems

Akito Arima, N. Yoshida, Joseph N. Ginocchio

Physics Letters BMay 1, 198160 citations

The Jordan-Wigner map in two dimensions is an exact lattice regularization of the $2\ensuremath{\pi}$-flux attachment to a hard-core boson (or spin

\frac{1}{2}

) leading to a composite fermion particle. When the spin-

\frac{1}{2}

model obeys ice rules this map preserves locality, namely, local Rohkshar-Kivelson (RK) models of spins are mapped onto local models of Jordan-Wigner composite fermions. Using this composite fermion dual representation of RK models we construct spin-liquid states by projecting Slater determinants onto the subspaces of the ice rules. Interestingly, we find that these composite fermions behave as ``dipolar'' partons for which the projective implementations of symmetries are very different from standard ``pointlike'' partons. We construct interesting examples of these composite Fermi-liquid states that respect all microscopic symmetries of the RK model. In the six-vertex subspace, we constructed a time-reversal and particle-hole-invariant state featuring two massless Dirac nodes, which is a composite fermion counterpart to the classic $\ensuremath{\pi}$-flux state of Abrikosov fermions in the square lattice. This state is a good ground-state candidate for a modified RK--type Hamiltonian of quantum spin ice. In the dimer subspace, we constructed a state featuring a composite Fermi surface but with nesting instabilities towards ordered phases such as the columnar state. We have also analyzed the low-energy emergent gauge structure. If one ignores confinement, the system would feature a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ low-energy gauge structure with two associated gapless photon modes, but with the composite fermion carrying gauge charge only for one photon and behaving as a gauge-neutral dipole under the other. These states are also examples of pseudoscalar

\text{U}(1)

spin liquids where mirror and time-reversal symmetries act as composite fermion particle-hole conjugations, and the emergent magnetic fields are even under such time-reversal or lattice mirror symmetries.