Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Spin-charge transformation of the Hubbard and t-J models

Johan Carlström

Published Jul 21, 2016• 0 citations
OpenAlex

Abstract

I derive a mapping of the Hubbard and t-J models onto a description in terms of spins and spin-less fermions. This transformation can be combined with the Fedotov-Popov fermionisation technique, where spin-1/2 systems are mapped onto two-component lattice fermions with imaginary chemical potential. The result is a generalisation of the Fedotov-Popov formulation to the case of finite doping that makes it possible to treat the Hubbard and t-J models as spin-models in the presence of a finite density of holes and doublons. While strongly interacting lattice fermions near half-filling is an extremely challenging problem, spin-systems can be efficiently treated with current simulation techniques.

Related papers

Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems

Johan Carlström

I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted Hilbert space. These constructions are based on spin-charge transformation, where the lattice fermions of the original model are mapped onto spins and spin-less fermions. This mapping can then be combined with Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions with imaginary chemical potential. The resulting models do not contain any large expansion parameters, even for strongly correlated systems. Also, they exhibit dramatically smaller corrections to the density matrix from nonlinear terms in the Hamiltonian. The combination of these two properties means that they can be addressed with diagrammatic methods, including simulation techniques based on stochastic sampling of diagrammatic expansions.

arXiv:1607.06293•Journal of Physics Condensed Matter•Jul 6, 2017•11 citations

From the Popov-Fedotov case to universal fermionization

Nikolay V. Prokof'ev, Boris V. Svistunov

We show that the Popov-Fedotov trick of mapping spin-1/2 lattice systems onto two-component fermions with imaginary chemical potential readily generalizes to bosons with a fixed (but not limited) maximal site occupation number as well as to fermionic Hamiltonians with various constraints on the site Fock states. In a general case, the mapping---fermionization---is on multicomponent fermions with many-body non-Hermitian interactions. Additionally, the fermionization approach allows one to convert large many-body couplings into single-particle energies, rendering the diagrammatic series free of large expansion parameters; the latter is essential for the efficiency and convergence of the diagrammatic Monte Carlo method.

arXiv:1103.3730•Physical Review B•Aug 11, 2011•14 citations

Derivation of the t−J model for finite doping

Simone A. Hamerla, Sebastian Duffe, Götz Silvester Uhrig

Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a $t\text{\ensuremath{-}}J$ model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the $t\text{\ensuremath{-}}J$ model is only known at half filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of $t\text{\ensuremath{-}}J$ model is determined as function of the doping $\ensuremath{\delta}$ and the ratio bandwidth $W$ over interaction $U$.

arXiv:1008.0522•Physical Review B•Dec 14, 2010•18 citations

Extension of the Popov-Fedotov method to arbitrary spin

O. Veits, R. Oppermann, M. Binderberger +1 more

The partition function and thermodynamic expectation values of a spin system with arbitrary spin quantum number are expressed by an exact fermionic representation on Fock space. Extending a suggestion of Popov and Fedotov, this is achieved by introducing a set of imaginary chemical potentials. Spin operators are replaced by usual bilinear combinations of Fermi operators satisfying the spin commutation relations.

Journal de Physique I•Apr 1, 1994•19 citations

Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model

Johan Carlström

Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionization of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite on-site repulsion and compare the results to controllable data obtained from numerical linked-cluster expansion. I find excellent agreement between the two methods, as well as rapid convergence of the diagrammatic series. I also report results for the momentum distribution and kinetic energy of the electrons.

arXiv:1709.06415•Physical review. B./Physical review. B•Feb 12, 2018•18 citations

Exact Transformation for Spin-Charge Separation of Spin- 1/2 Fermions without Constraints

Stellan S. Ostlund, Mats Granath

We demonstrate an exact local transformation which maps a purely Fermionic many-body system to a system of spinful bosons and spinless fermions, demonstrating a possible path to a non-Fermi-liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a chargelike quasicharge fermion and a spinlike quasispin Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.

arXiv:cond-mat/0507242•Physical Review Letters•Feb 15, 2006•31 citations
I derive a mapping of the Hubbard and t-J models onto a description in terms of spins and spin-less fermions. This transformation can be combined with the Fedotov-Popov fermionisation technique, where spin-1/2 systems are mapped onto two-component lattice fermions with imaginary chemical potential. The result is a generalisation of the Fedotov-Popov formulation to the case of finite doping that makes it possible to treat the Hubbard and t-J models as spin-models in the presence of a finite density of holes and doublons. While strongly interacting lattice fermions near half-filling is an extremely challenging problem, spin-systems can be efficiently treated with current simulation techniques.
I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted Hilbert space. These constructions are based on spin-charge transformation, where the lattice fermions of the original model are mapped onto spins and spin-less fermions. This mapping can then be combined with Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions with imaginary chemical potential. The resulting models do not contain any large expansion parameters, even for strongly correlated systems. Also, they exhibit dramatically smaller corrections to the density matrix from nonlinear terms in the Hamiltonian. The combination of these two properties means that they can be addressed with diagrammatic methods, including simulation techniques based on stochastic sampling of diagrammatic expansions.
We show that the Popov-Fedotov trick of mapping spin-1/2 lattice systems onto two-component fermions with imaginary chemical potential readily generalizes to bosons with a fixed (but not limited) maximal site occupation number as well as to fermionic Hamiltonians with various constraints on the site Fock states. In a general case, the mapping---fermionization---is on multicomponent fermions with many-body non-Hermitian interactions. Additionally, the fermionization approach allows one to convert large many-body couplings into single-particle energies, rendering the diagrammatic series free of large expansion parameters; the latter is essential for the efficiency and convergence of the diagrammatic Monte Carlo method.
Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a $t\text{\ensuremath{-}}J$ model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the $t\text{\ensuremath{-}}J$ model is only known at half filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of $t\text{\ensuremath{-}}J$ model is determined as function of the doping $\ensuremath{\delta}$ and the ratio bandwidth WWW over interaction UUU.
Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionization of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite on-site repulsion and compare the results to controllable data obtained from numerical linked-cluster expansion. I find excellent agreement between the two methods, as well as rapid convergence of the diagrammatic series. I also report results for the momentum distribution and kinetic energy of the electrons.
We demonstrate an exact local transformation which maps a purely Fermionic many-body system to a system of spinful bosons and spinless fermions, demonstrating a possible path to a non-Fermi-liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a chargelike quasicharge fermion and a spinlike quasispin Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.