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

Bulletin of the American Physical Society

A Generalized Slave-Particle Method

Alexandru Bogdan Georgescu, Sohrab Ismail‐Beigi

Published Mar 2, 2015• 0 citations
OpenAlex

Abstract

We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model at weak correlation strength by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.

Related papers

Generalized slave-particle method for extended Hubbard models

Alexandru Bogdan Georgescu, Sohrab Ismail‐Beigi

We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model, where it systematically overestimates the importance of electronic correlation effects for weak interaction strength, by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.

arXiv:1506.03515•Physical Review B•Dec 8, 2015•21 citations

Slave-spin approach to the strongly correlated systems

Mardani, Masoud, Mohammad-Sadegh Vaezi, Abolhassan Vaezi

In this paper, we develop a new type of slave particle method which is similar to the slave rotor model except that the quantum rotor is substituted by a spin one slave particle. The spin-one slave particle itself can be represented in terms of Schwinger bosons/fermions. This approach is more conveniently applicable to the strongly correlated Hamiltonians with on-site Hubbard interaction and resolves the limitations of using the slave rotor model as well as the Anderson-Zou slave particle technique. For instance, the mean-field parameters of the slave spin method do not vanish above the Mott transition and this approach is smoothly connected to the non-interacting limit. As an example, we study the phase diagram of the Kane-Mele-Hubbard model using our current approach. In the absence of the spin-orbit interaction, the Mott transition occurs at $U_c ~ 3 t_1$. Several aspects of the slave spin method, its gauge theory and various possible mean-field states associated with this approach have been discussed.

arXiv:1111.5980•Nov 25, 2011•3 citations

Symmetry Breaking in Slave-Particle Methods for the Hubbard Model

Alexandru Bogdan Georgescu, Sohrab Ismail‐Beigi

We describe a theoretical approach for finding spontaneously symmetry-broken electronic phases due to strong electronic interactions when using recently developed slave-particle (slave-boson) approaches based on occupation numbers. We describe why, to date, spontaneous symmetry breaking has proven difficult to achieve in such approaches. We then provide a total-energy based approach for introducing auxiliary symmetry breaking fields into the solution of the slave-particle problem that leads to lowered total energies for symmetry broken phases. We point out that not all slave-particle approaches yield to energy lowering: the slave-particle model being used must explicitly describe the degrees of freedom that break symmetry. Finally, our total energy approach permits us to greatly simplify the formalism used to achieve a self-consistent solution between spinon and slave modes while increasing numerical stability and greatly speeding up the calculations.

•Feb 11, 2017•0 citations

Benchmarking the simplest slave-particle theory with Hubbard dimer*

Wei-Wei Yang, Hong-Gang Luo, Yin Zhong

Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal–insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z 2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z 2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods: (i) slave-spin method on mean-field level, (ii) slave-spin method with gauge constraint, and (iii) the exact solution as a benchmark. We find that, protected by the particle–hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space. These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.

arXiv:1809.08528•Chinese Physics B•Aug 23, 2019•5 citations

Unified Slave Boson Representation of Spin and Charge Degrees of Freedom for Strongly Correlated Fermi Systems

Raymond Frésard, P. Wölfle

We consider a slave boson representation of lattice electrons in terms of bosons for the empty, singly and doubly occupied site. The approach generalizes an earlier formulation by Kotliar and Ruckenstein. As examples the Hubbard model and the t-J model are considered. The emphasis is on a detailed derivation and discussion of the formal aspects. Simple meanfield solutions are discussed for illustrative purposes.

International Journal of Modern Physics B•Mar 1, 1992•108 citations

SPIN-CARRYING SLAVE BOSON REPRESENTATION FOR STRONGLY CORRELATED FERMION SYSTEMS

P. Wölfle

We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.

International Journal of Modern Physics B•Dec 1, 1989•0 citations
We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model at weak correlation strength by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.
We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model, where it systematically overestimates the importance of electronic correlation effects for weak interaction strength, by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.
In this paper, we develop a new type of slave particle method which is similar to the slave rotor model except that the quantum rotor is substituted by a spin one slave particle. The spin-one slave particle itself can be represented in terms of Schwinger bosons/fermions. This approach is more conveniently applicable to the strongly correlated Hamiltonians with on-site Hubbard interaction and resolves the limitations of using the slave rotor model as well as the Anderson-Zou slave particle technique. For instance, the mean-field parameters of the slave spin method do not vanish above the Mott transition and this approach is smoothly connected to the non-interacting limit. As an example, we study the phase diagram of the Kane-Mele-Hubbard model using our current approach. In the absence of the spin-orbit interaction, the Mott transition occurs at Uc 3t1U_c ~ 3 t_1Uc​ 3t1​. Several aspects of the slave spin method, its gauge theory and various possible mean-field states associated with this approach have been discussed.
We describe a theoretical approach for finding spontaneously symmetry-broken electronic phases due to strong electronic interactions when using recently developed slave-particle (slave-boson) approaches based on occupation numbers. We describe why, to date, spontaneous symmetry breaking has proven difficult to achieve in such approaches. We then provide a total-energy based approach for introducing auxiliary symmetry breaking fields into the solution of the slave-particle problem that leads to lowered total energies for symmetry broken phases. We point out that not all slave-particle approaches yield to energy lowering: the slave-particle model being used must explicitly describe the degrees of freedom that break symmetry. Finally, our total energy approach permits us to greatly simplify the formalism used to achieve a self-consistent solution between spinon and slave modes while increasing numerical stability and greatly speeding up the calculations.
Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal–insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z 2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z 2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods: (i) slave-spin method on mean-field level, (ii) slave-spin method with gauge constraint, and (iii) the exact solution as a benchmark. We find that, protected by the particle–hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space. These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.
We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.