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.
The treatment of intershell interactions remains a major challenge in the theoretical description of strongly correlated materials. Most previous approaches considered the influence of intershell interactions at best in a static fashion, neglecting dynamic effects. In this work, we propose a slave-rotor method that goes beyond this approximation by incorporating the effect of intershell interactions in a dynamic manner. Our method is derived and implemented as a quantum impurity solver in the context of dynamical mean field theory and benchmarked on a two-orbital model system. The results from…
We revisit the Kotliar-Ruckenstein (KR) slave boson saddle point evaluation for a two-site correlated electron model. As the model can be solved analytically, it is possible to compare the KR saddle point results to the exact many particle levels. The considered two site cluster mimics an infinite-$U$ single-impurity Anderson model with a nearest neighbor Coulomb interaction: one site is strongly correlated with an infinite local Coulomb repulsion which hybridizes with the second site, on which the local Coulomb repulsion vanishes. Making use of the flexibility of the representation we introdu…
The standard mean field slave-boson solution for the infinite-$U$ Hubbard model is revised. A slightly modified version is proposed which includes properly the incoherent contribution of the localized states. In contrast to the standard mean field result, this new proposed solution defines a unique spectral function to be used in the calculation of local and not local quantities, and satisfies the correct thermodynamic relations. The same approach is applied also to the mean field approximation in terms of Hubbard operators. As a byproduct of this analysis, Luttinger's theorem is shown to be f…
The multiorbital Hubbard model is expressed in terms of quantum phase variables (``slave rotors'') conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a ``preformed'' Mott gap in the single-particle density of states. The slave- rotor formalism allows to go beyond the local description and take i…
We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the …
We show that the physical subspace in the Z2-slave-spin theory is conserved under the time evolution of the system. Thus, when restricted to the physical subspace, this representation gives a complete and consistent description of the original problem. In addition, we review two known examples from the existing literature in which the projection onto the physical subspace can be relaxed: (i) the non-interacting limit in any dimension at half filling and (ii) the interacting model in the infinite dimensional limit at half filling. In both cases, physical observables are correctly obtained witho…
We present a mean field treatment of a strongly correlated model of electrons in a three-dimensional anisotropic system. The mass of the bare electrons is larger in one spatial direction (the c-axis direction), than in the other two (the ab-planes). We use a slave fermion decomposition of the electronic degrees of freedom and show that there is a transition from a deconfined to a confined phase in which there is no coherent band formation along the c-axis.
In a recent Letter, Nayak argued that slave partices are always confined in gauge theories of strongly-correlated electron systems like the t-J model. The argument mostly relies on Elitzur's theorem and the fact that the effective gauge theory under discussion is at infinite coupling. On the other hand, in the previous papers we studied dynamics of the gauge theory of the t-J model showing that the slave particles are in the Coulomb phase below certain critical temperature T{CSS} that depends on hole doping. We comment on the discrepancy between the results in two papers.
The combination of the local-density approximation (LDA) with the rotationally invariant slave-boson theory (RISB) is used to investigate the realistic correlated electronic structure of Sr$_3$Ru$_2$O$_7$. From Wannier-downfolding the low-energy band structure to a three-band model for the Ru($t_{2g}$) states, the interacting problem is solved including intra- and inter-orbital Hubbard terms as well as spin-flip and pair-hopping interactions. Therewith it is possible to obtain valuable insight into the orbital occupations, relevant local spin multiplets and the fermiology with increasing corre…
Consistent gauge theories for the slave particle representation of the strongly correlated $t$-$J$ model
College of Science, University of Shanghai for Science and Technology（上海理工大学理学院）；Institute of Theoretical Physics, Chinese Academy of Science（中国科学院理论物理研究所）；Department of Physics, Fudan University（复旦大学物理系）；Department of Physics, Institute of Solid State Physics and Center for Computational Sciences, Sichuan Normal University（四川师范大学物理系、固体物理研究所及计算科学中心）
We review a representation of Hubbard-like models that is based on auxiliary pseudospin variables. These pseudospins refer to the local charge modulo two in the original model and display a local Z_2 gauge freedom. We discuss the associated mean-field theory in a variety of different contexts which are related to the problem of the interaction-driven metal-insulator transition at half-filling including Fermi surface deformation and spectral features beyond the local approximation. Notably, on the mean-field level, the Hubbard bands are derived from the excitations of an Ising model in a transv…
We calculate the phase diagram of the topological honeycomb model in the presence of strong interactions. We concentrate on half filling and employ a ${\mathbb Z}_{2}$ slave-spin method to find a band insulator with staggered density, a spin-density-wave and a Mott insulating phase. Both the band insulator and the spin-density wave come in various topological varieties. Finally, we calculate the response function relevant for lattice modulation spectroscopy with cold atomic gases in optical lattices.
We extend the rotationally invariant formulation of the slave-boson method to superconducting states. This generalization, building on the recent work by Lechermann et al. [Phys. Rev. B {\bf 76}, 155102 (2007)], allows to study superconductivity in strongly correlated systems. We apply the formalism to a specific case of strongly correlated superconductivity, as that found in a multi-orbital Hubbard model for alkali-doped fullerides, where the superconducting pairing has phonic origin, yet it has been shown to be favored by strong correlation owing to the symmetry of the interaction. The metho…
I reexamine the Nayak's criticism [Phys. Rev. Lett. 85, 178 (2000); 86, 943 (2001).] on the U(1) gauge theory approach to the strongly correlated systems. Contrary to his conclusion, the arbitrariness of the charge assignment observed by him does not contradict the possibility of a deconfinement. Should the deconfinement occur, the deconfined slave particle carries an effective fractional charge, which is independent of the arbitrary assignment but is rather determined dynamically.
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 b…
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, $\mathbb{Z}_2$ slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the…
We show that slave particles are always confined in U(1) gauge theories of interacting electron systems. Consequently, the low-lying degrees of freedom are different from the slave particles. This is done by constructing a dual formulation of the slave-particle representation in which the no-double occupany constraint becomes linear and, hence, soluble. Spin-charge separation, if it occurs, is due to the existence of solitons with fractional quantum numbers.
The slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case of the hopping integral t equal to the correlated hopping integral X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any values of X and any electron concentration n. At the half-filled band (n=1) a direct transition from the superconductor to the M…
The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure. Additionally, the extraction of effective low-energy theories from the generalized many-body representation is highly desirable. In this respect, the rotational-invariant slave boson (RISB) approach in its mean-field formulation enables versatile access to correlated lattice problems. However in its original form, due to numerical complexity, the RISB approach…
We propose a new method of solving a class of mean-field (MF) models, which is based on the Maximum Entropy (MaxEnt) principle with additional constraints included. Next, we show equivalence of our method when applied to the Gutzwiller approximation (GA), with the mean-field slave-boson (SB) formalism (on the example of the single-band Hubbard model). This equivalence provides thus an alternative justification of the results obtained within the SB approach which, however, contains ad hoc assumptions to position it in agreement with GA. Our approach implies that all predictions of the MF SB met…
Mott transition plays a key role in strongly correlated physics but its nature is not yet fully understood. Motivated by recent development of Schwinger boson approach for the Kondo lattice, we propose in this work a novel slave fermion algorithm to study the Mott transition. Upon local approximation, our method yields a phase diagram with a zero-temperature continuous (Mott) metal-insulator transition at finite Coulomb interaction $U$ for the half-filled one-band Hubbard model on a square lattice, and the resistivity exhibits a critical scaling around the quantum Widom line. We argue that the…
Spin Dynamics from Niu-Kleinman Adiabatic Approach and Slave Boson Mean Field Theory
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所（北京凝聚态物理国家研究中心））；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；New Cornerstone Science Laboratory, Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（新基石科学实验室，中国科学院物理研究所（北京凝聚态物理国家研究中心））
Building on work by Florens and Georges, we formulate and study a self-consistent slave rotor mean field theory for strongly correlated systems. This approach views the electron, in the strong correlation regime, as a composite of a neutral spinon and a charged rotor field. We solve the coupled spinon-rotor model self-consistently using a cluster mean field theory for the rotors and various ansatzes for the spinon ground state. We illustrate this approach with a number of examples relevant to ongoing experiments in strongly correlated electronic systems such as: (i) the phase diagram of the is…
Effective gauge theories based on slave particle construction are widely used to describe quantum number fractionalization in strongly correlated electron systems. However, even setting aside the intense debates on the confinement issue of the slave particles, there are still significant conflicts between theory and experiment. In particular, a $T^{2/3}$ specific heat anomaly has been predicted as the key signature of low-lying gauge fluctuation in a $U(1)$ spin liquid with a large spinon Fermi surface, which is however never observed. Here we show that such an anomaly is actually an artifact …
The U(1) holon-pair boson theory of Lee and Salk(Phys. Rev. B 64, 052501 (2001)) is applied to investigate the quantum scaling behavior of optical conductivity in the two dimensional systems of strongly correlated electrons. We examine the role of both the gauge field fluctuations and spin pair excitations on the w/T scaling behavior of the optical conductivity. It is shown that the gauge field fluctuations but not the spin pair excitations are responsible for the scaling behavior in the low frequency region w/T <<1. Importance for the contribution of the nodal spinons to the Drude peak is dis…
A U(1) slave-spin representation is introduced for multi-orbital Hubbard models. As with the $Z_2$ form of L. de'Medici et al. (Phys. Rev. B 72, 205124 (2005)), this approach represents a physical electron operator as the product of a slave spin and an auxiliary fermion operator. For non-degenerate multi-orbital models, our U(1) approach is advantageous in that it captures the non-interacting limit at the mean-field level. For systems with either a single orbital or degenerate multiple orbitals, the U(1) and $Z_2$ slave-spin approachs yield the same results in the slave-spin-condensed phase. I…
Recently, we have elucidated the physics of electron fractionalization in strongly interacting electron systems using a $Z_2$ gauge theory formulation. Here we discuss the connection with the earlier U(1) gauge theory approaches based on the slave boson mean field theory. In particular, we identify the relationship between the holons and Spinons of the slave-boson theory and the true physical excitations of the fractionalized phases that are readily described in the $Z_2$ approach.
Recent studies of dynamical screening of the electronic Coulomb interactions in solids have revived interest in lattice models of correlated fermions coupled to bosonic degrees of freedom (Hubbard-Holstein-type models). We propose a dynamical mean-field-based approach to dynamically screened Coulomb interactions. In the effective Anderson-Holstein model, a transformation to slave rotors [S. Florens and A. Georges, Phys. Rev. B 66, 165111 (2002)] is performed to decouple the dynamical part of the interaction. This transformation allows for a systematic derivation and analysis of recently introd…
Slave-spin mean-field theory, a light and accurate technique to model electronic correlations in Fermi-liquid phases of multi-orbital materials, is pedagogically exposed in this chapter, with a focus on its recent successful application to the physics of Iron-based superconductors. Beside introducing electronic correlations and recalling the Fermi-liquid phenomenology, the manuscript accompanies the step-by-step explanation of the slave-spin technique with a set of useful complements providing analytical insight into Mott and Hund's physics, which are at the heart of the physics of strongly co…
We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight $Z$ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature $T_\textrm{coh}$ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling…
The long-standing issue of the competition between the magnetic field and the Kondo effect, favoring, respectively, triplet and singlet ground states is addressed using a cluster slave-rotor mean field theory for the Hubbard model and its spin-correlated, spin-frustrated extensions in 2 dimension. The metamagnetic jump is established and compared with earlier results of dynamical mean-field theory. The present approach also reproduces the emergent super-exchange energy scale in the insulating side. A scaling is found for the critical Zeeman field in terms of the intrinsic coherence scale just …
We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on fluctuation around rotationally-invariant slave-boson saddle-point. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hund's metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels…
We investigate the correlated electrons in the magic-angle twisted bilayer graphene by using the slave-rotor mean-field theory. Owing to the extended figure of Wannier orbitals, we study the two-orbital cluster Hubbard model with spin-valley fourfold degeneracy, focusing around half filling of valence bands below the neutrality point. The theory predicts multiple Mott insulator phases at fractional fillings not only for integer charges per moir{é} site, and it demonstrates that long-range electron hopping is highly suppressed because multiple-charge excitations are induced. Furthermore, the Ke…
The cluster slave-spin method is introduced to systematically investigate the solutions of the Hubbard model including the symmetry-broken phases. In this method, the electron operator is factorized into a fermioninc spinon describing the physical spin and a slave-spin describing the charge fluctuations. Following the $U(1)$ formalism derived by Yu and Si [Phys. Rev. B 86, 085104 (2012)], it is shown that the self-consistent equations to explore various symmetry-broken density wave states can be constructed in general with a cluster of multiple slave-spin sites. We employ this method to study …
In this paper, we investigate the topological Hubbard model - the spinful Haldane model with on-site interaction on honeycomb lattice with spin rotation symmetry by using slave-rotor approach and find that chiral spin liquid exists in such a correlated electron system of the intermediate coupling region. By considering the anyon nature of excitations, chiral spin liquid may be the ground state of the topological Hubbard model. The low energy physics is basically determined by its Chern-Simons gauge theory.
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spi…
We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This iterative scheme, dubbed Natural Orbitalization (NOization)…
We study the ground state of the Hubbard model on a square lattice with two degenerate orbitals per site and at integer fillings as a function of onsite Hubbard repulsion $U$ and Hund's intra-atomic exchange coupling $J$. We use a variational slave-spin mean field (VSSMF) method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism, thus making the method more powerful to study strongly correlated electron physics. The results show that at half-filling, the ground state at smaller $U$ is a Slater antiferromagnet (AF) with su…
We investigate the superconductivity in the $t-J-U$ model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of the spinons $Δ_f$ and the Cooper pairing gap of the electrons $Δ_{SC} = ZΔ_f$, where $Z$ is the quasiparticle weight. Furthermore, we find that the nature of the superconducting state depends crucially on the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by $Z$ but the its pairing ter…
A new slave-spin representation of fermion operators has recently been proposed for the half-filled Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. The resulting spin problem can be solved using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength $U$ is infinite, this…
It has been recently shown that the particle-hole symmetric Anderson impurity model can be mapped onto a $Z_2$ slave-spin theory without any need of additional constraints. Here we prove by means of Numerical Renormalization Group that the slave-spin behaves in this model like a two-level system coupled to a sub-ohmic dissipative environment. It follows that the $Z_2$ symmetry gets spontaneously broken at zero temperature, which we find can be identified with the on-set of Kondo coherence, being the Kondo temperature proportional to the square of the order parameter. Since the model is numeric…
We present the simplest model to which one can apply the supersymmetric Hubbard operators recently introduced. For the atomic model, $H=-E_d X_{00}$, where $X_{00} = |0><0|$ is a Hubbard operator and $E_d$ is the energy of the localized spin level, we show how one can develop exact solutions for the entropy and heat capacity as a function of temperature. With this gold standard we are able to develop a controlled approximation scheme to field theoretically treat the susy approximation at the level of mean field + gaussian corrections and test its accuracy against the widely used slave boson an…
We introduce a strongly correlated mean-field theory of the ionic Hubbard model on the triangular lattice with alternating stripes of site energy using Barnes-Coleman slave bosons. We study the paramagnetic phases of this theory at three quarters filling, where it is a model of Na_0.5CoO_2, Rb_0.5CoO_2, and K_0.5CoO_2. This theory has two bands of fermionic quasi-particles: one of which is filled or nearly filled and hence weakly correlated; the other is half-filled or nearly half-filled and hence strongly correlated. Further results depend strongly on the sign of the hopping integral, t. The …
A novel gapped metallic state coined orthogonal Dirac semimetal is proposed in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of Hubbard model. This state corresponds to the disordered phase of slave-spin and has the same thermaldynamical and transport properties as usual Dirac semimetal but its singe-particle excitation is gapped and has nontrivial topological order due to the $Z_{2}$ gauge structure. The quantum phase transition from this orthogonal Dirac semimetal to usual Dirac semimetal is described by a mean-field decoupling with complementary fluctuation analysis an…
Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner/Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However many experimental studies, e.g. of (de)magnetization processes, focus on itinerant local-moment materials such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space imp…
The spectrum of the strongly correlated systems usually shows resonant peaks at finite energy, with examples in the 115 Ce family which are reproduced by the dynamical mean-field theory. A similar structure has been seen recently in the orbitally selective Mott (OSM) phase of two-band model, known as doublon-holon bound state, with implications on the fate of such phase in the zero Hund's coupling limit. We show that these features can be captured with the slave-particle methods once their Hilbert space is taken into account. We use slave-spin calculations, justifiable in the limit of large di…
Slave rotor mean field (SRMF) theory is employed to study exciton formation in the extended Falicov-Kimball Model (EFKM). In this theory, charge and spin (or orbital) degrees are treated as independent degrees of freedom, coupled by a constraint. Using this formalism in single as well as cluster extension, we capture the effective many body scales beyond conventional mean-field theory. While the formation of exciton is favored by the interband hybridization $V$, it is strongly influenced by the on-site Coulomb interaction $U$. Beyond a critical hybridization, there is a condensation of exciton…
Various auxiliary-particle approaches to treat electron correlations in many-electron models are analyzed. Applications to copper-oxide layered systems are discussed. The ground-state magnetic phase diagrams are considered within the Hubbard and $s$-$d$ exchange (Kondo) models for square and simple cubic lattices vs. band filling and interaction parameter. A generalized Hartree-Fock approximation is employed to treat commensurate ferro-, antiferromagnetic, and incommensurate (spiral) magnetic phases, and also magnetic phase separation. The correlations are taken into account within the Hubbard…
Fermionizing the charge sector and bosonizing the spin part in the SU(2) slave-boson theory, we derive an effective field theory for dynamics of doped holes in the antiferromagnetically correlated spin background, where spin fluctuations are described by an SO(5) Wess-Zumino-Witten (WZW) theory while dynamics of doped holes is characterized by QED$_{3}$ with a chemical potential term. An important feature of our effective field theory is the coupling term between valance bond fluctuations and doped holes. Considering that valance bond fluctuations are deeply related with monopole excitations o…
We determine the localization threshold in a partially filled and orbitally degenerate model of correlated electrons. Particular emphasis is put on a non-integer band filling, when the system decomposes into the localized and the itinerant subsystems; this situation is described by an effective s-d model. A simultaneous transition to the ferromagnetic state is discussed as driven by the Hund's rule coupling. Dependence of the quasiparticle mass on the spin direction appears naturally in the ferromagnetic phase and is attributed to the electron correlation effects, as is also a metamagnetic tra…
