A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z$_{2}$ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z$_{2}$, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.
We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in presence of Hund's coupling interaction. By analytical analysis of Hamiltonian, we show that the locking of the two orbitals vs.\,orbital-selective Mott transition can be formulated within a Landau-Ginzburg framework. By applying the slave-spin mean-field to impurity problem, we are able to make a correspondence between impurity and lattice. We also consider the stability of the orbital selective Mott phase to the hybridization between the orbitals and study the limitations of the sla…
A new mean field theory is proposed for the Mott transition in the Hubbard model based on the slave rotor representation of the electron operator. This theory provides a better description of the role of the long range charge correlation in the Mott insulating state and offers a good estimation of the critical correlation strength for the Mott transition. We have constructed a new variational wave function for the Mott insulating state based on this new slave rotor mean field theory. We find this new variational wave function outperforms the conventional Jastrow type wave function with long ra…
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…
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…
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $z$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $1/\sqrt{z}$, and becomes exact on the infinite-$z$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with …
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…
Metal-insulator transitions in a three-component Falicov-Kimball model are investigated within the Kotliar-Ruckenstein slave boson mean-field approach. The model describes a mixture of two interacting fermion atom species loaded into an optical lattice at ultralow temperature. One species is two-component atoms, which can hop in the optical lattice, and the other is single-component atoms, which are localized. Different correlation-driven metal-insulator transitions are observed depending on the atom filling conditions and local interactions. These metal-insulator transitions are classified by…
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…
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 t…
We investigate how the antiferromagnetic Mott insulator evolves into the d-wave BCS superconductor through hole doping. Allowing spin fluctuations in the strong coupling approach, we find a spin-gapped incoherent metal with preformed pairing as an intermediate phase between the antiferromagnetic Mott insulator and d-wave superconductor. This non-Fermi liquid metal is identified with an infrared stable fixed point in the spin-decomposition gauge theory, analogous to the spin liquid insulator in the slave-boson gauge theory. We consider the single particle spectrum and dynamical spin susceptibil…
We present a theoretical approach to describing the Mott transition of electrons on a two dimensional lattice that begins with the low energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations which correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a prior assumptions about other Fermi surface shape fluctuations. Buil…
Time reversal protected three dimensional (3D) topological paramagnets are magnetic analogs of the celebrated 3D topological insulators. Such paramagnets have a bulk gap, no exotic bulk excitations, but non-trivial surface states protected by symmetry. We propose that frustrated spin-1 quantum magnets are a natural setting for realising such states in 3D. We describe a physical picture of the ground state wavefunction for such a spin-1 topological paramagnet in terms of loops of fluctuating Haldane chains with non-trivial linking phases. We illustrate some aspects of such loop gases with simpl…
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…
We study how to incorporate Mott physics in the BCS-type superconductor, motivated from the fact that high $T_c$ superconductivity results from a Mott insulator via hole doping. The U(1) slave-rotor representation was proposed to take local density fluctuations into account non-perturbatively, describing the Mott-Hubbard transition at half filling. Since this decomposition cannot control local pairing fluctuations, the U(1) slave-rotor representation does not give a satisfactory treatment for charge fluctuations. Extending the U(1) slave-rotor representation, we introduce an SU(2) slave-rotor …
We employ the cluster slave-spin method to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $δ$ and coupling strength $U$ being its parameters. In addition to a crossover reflected in the behavior of the antiferromagnetic gap $Δ_{\text{AFM}}$, this property can also be observed in the energetics of the cluster slave-spin Hamiltonian -- the antiferromagnetism at small $U$ is due to the potential energy gain while that in the strong coupling limit is driven by the kinetic energy gain, which is consistent with the results from the cluster…
Motivated by the debate of spin-density-wave (SDW) versus local-moment (LM) picture in the iron-based superconducting (FeSC) materials, we consider a two-band orbital-symmetric Hubbard model in which there is robust Fermi surface nesting at $(π,0)$. We obtain the phase diagram of such system by a mean-field slave-rotor approach, in which the Fermi surface nesting and the SDW order are explicitly taken into account via a natural separation of scale between the Hund's coupling and the Coulomb interaction. We find that for a sizable range of Hund's coupling the Mott transition acquires a strong f…
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…
Particle-hole continuum (PHC) for massive Dirac fermions in presence of short range interactions, provides an unprecedented opportunity for formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel in undoped system. Both poles are close in energy and are separated from thec continuum of free particle-hole excitations by an energy scale of the order of gap parameter $Δ$. They both disperse linearly with two different velocities reminiscent of spin-charge separation in Luttinger liquids. When the strength of Hubbard interactions is stronger t…
$^{13}$C nuclear magnetic resonance measurements were performed for a single-component molecular material Zn(tmdt)$_{2}$, in which tmdt's form an arrangement similar to the so-called $κ$-type molecular packing in quasi-two-dimensional Mott insulators and superconductors. Detailed analysis of the powder spectra uncovered local spin susceptibility in the tmdt $π$ orbitals. The obtained shift and relaxation rate revealed the singlet-triplet excitations of the $π$ spins, indicating that Zn(tmdt)$_{2}$ is a spin-gapped Mott insulator with exceptionally large electron correlations compared to conven…
We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the…
The issues of single particle coherence and its interplay with singlet pairing are studied within the slave boson gauge theory of a doped Mott insulator. Prior work by one of us (T. Senthil, arXiv:0804.1555) showed that the coherence scale below which Landau quasiparticles emerge is parametrically lower than that identified in the slave boson mean field theory. Here we study the resulting new non-fermi liquid intermediate temperature regime characterized by a single particle scattering rate that is linear in temperature ($T$). In the presence of a d-wave pair amplitude this leads to a pseudoga…
Within the framework of a mean-field approach the Mott-Hubbard phase transition is considered in the Hubbard and Falicov-Kimball models for half-filled occupation. It is shown that a static Z_2-field forms an insulator state on the lattice with a double cell, its strength is determined by the Hubbard interaction. An uniform configuration of the Z_2-field corresponds to a gapless spin liquid state, the configuration, at which the lattice with a double cell is formed, corresponds to a gapped fermion liquid, fermions move in this field. Due to the presence of a static field in an insulator state,…
Recently, a concept of orthogonal metal has been introduced to reinterpret the disordered state of slave-spin representation in the Hubbard model as an exotic gapped metallic state. We have extended this concept to study the slave-spin representation of Hubbard model on the honeycomb lattice.[Phys. Rev. B \textbf{86}, 165134 (2012)] It is found that a novel gapped metallic state coined orthogonal Dirac semimetal is identified. Such state corresponds to the disordered phase of slave-spin and has the same thermal-dynamical and transport properties as Dirac semimetal but its singe-particle excita…
The Mott insulator is the quintessential strongly correlated electronic state. We obtain complete insight into the physics of the two-dimensional Mott insulator by extending the slave-fermion (holon-doublon) description to finite temperatures. We first benchmark its predictions against state-of-the-art quantum Monte Carlo simulations, demonstrating quantitative agreement. Qualitatively, the short-ranged spin fluctuations both induce holon-doublon bound states and renormalize the charge sector to form the Hubbard bands. The Mott gap is understood as the charge gap renormalized downwards by thes…
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.
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…
The infinite dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a $Z_2$ gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local $Z_2$ gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactl…
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…
We propose the concept of "hybridization-switching induced Mott transition" which is relevant to a broad class of ABO$_3$ perovskite materials including BiNiO$_3$ and PbCrO$_3$ which feature extended $6s$ orbitals on the A-site cation (Bi or Pb), and A-O covalency induced ligand holes. Using {\it ab initio} electronic structure and slave rotor theory calculations, we show that such systems exhibit a breathing phonon driven A-site to oxygen hybridization-wave instability which conspires with strong correlations on the B-site transition metal ion (Ni or Cr) to induce a Mott insulator. These Mott…
We discuss the issue of phase separation in the SU(2) slave boson theory of Wen and Lee of the doped Mott insulator. It is shown that the constraint structure of the theory leads to the interpretation of the holons to have hard-core interactions, which is demonstrated further by studying the empty limit (no electrons). Surprisingly, with hard-core interactions even the empty limit is described well by the slave-boson theory, both as an energy density and with the regard to dynamical properties. The consequences are investigated in the overdoped superconducting regime, where both phase separati…
Dynamics of magnetic moments near the Mott metal-insulator transition is investigated by a combined slave-rotor and Dynamical Mean-Field Theory solution of the Hubbard model with additional fully-frustrated random Heisenberg couplings. In the paramagnetic Mott state, the spinon decomposition allows to generate a Sachdev-Ye spin liquid in place of the collection of independent local moments that typically occurs in the absence of magnetic correlations. Cooling down into the spin-liquid phase, the onset of deviations from pure Curie behavior in the spin susceptibility is found to be correlated t…
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
The electronic properties of Mott insulators realized in (111) bilayers of perovskite transition-metal oxides are studied. The low-energy effective Hamiltonians for such Mott insulators are derived in the presence of a strong spin-orbit coupling. These models are characterized by the antiferromagnetic Heisenberg interaction and the anisotropic interaction whose form depends on the $d$ orbital occupancy. From exact diagonalization analyses on finite clusters, the ground state phase diagrams are derived, including a Kitaev spin liquid phase in a narrow parameter regime for $t_{2g}$ systems. Slav…
There is increasing recognition that the multiorbital nature of the 3d electrons is important to the proper description of the electronic states in the normal state of the iron-based superconductors. Earlier studies of the pertinent multiorbital Hubbard models identified an orbital-selective Mott phase, which anchors the orbital-selective behavior seen in the overall phase diagram. An important characteristics of the models is that the orbitals are kinetically coupled -- i.e. hybridized -- to each other, which makes the orbital-selective Mott phase especially nontrivial. A U(1) slave-spin meth…
We introduce a valence-bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. The calculated tunneling and photoemission spectra are consistent with the phenomenology of the normal state of cuprates.…
We study the Kane-Mele-Hubbard model both at half-filling and away from half-filling using a slave-boson mean-field approach at zero temperature. We obtain a phase diagram at half-filling and discuss its connection to recent results from quantum Monte Carlo, slave-rotor, and $Z_2$ mean-field studies. In particular, we find a small window in parameter space where a spin liquid phase with gapped spin and charge excitations reside. Upon doping, we show the spin liquid state becomes a superconducting state by explicitly calculating the singlet pairing order parameters. Interestingly, we find an "o…
We reformulate the time-dependent Gutzwiller approximation by M. Schiró and M. Fabrizio [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a sp…
The cluster slave-spin method is implemented to research the ground state properties of the honeycomb lattice Hubbard model with doping $δ$ and coupling $U$ being its parameters. At half-filling, a single direct and continuous phase transition between the semi-metal and antiferromagnetic (AFM) insulator is found at $U_{\text{AFM}}=2.43t$ that is in the Gross-Neveu-Yukawa universality class, where a relation between the staggered magnetization $M$ and the AFM energy gap $Δ_{\text{AFM}}$ is established as $M \propto Δ_{\text{AFM}}$, compared to $M \propto Δ_{\text{AFM}} ( \ln{Δ_{\text{AFM}}})^2$…
We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\boldsymbol Q = (π, π), (0, π)$, and $(0, 0)$ we find incommensurate phases where the ordering wave vectors $\boldsymbol Q = (Q, Q)$, and $(Q, π)$ vary continuously with filling, interaction strength or temperature. The…
In this paper we generalized the slave-particle technique to study the phase diagram of the Hubbard model on honeycomb lattice which may contain charge fluctuations. For large $U$, we have antiferromagnetic order phase. As we decrease $U$ below $U_{c2}\simeq 3t$, the system undergoes a first order phase transition into a gapped spin rotation invariant phase. Under a semiclassical approximation of the slave-particle approach, we find that such phase breaks the translation symmetry, the parity and the lattice rotation symmetry. However, beyond the semiclassical approximation, a $Z_2$ spin liquid…
We present the influence of spin correlation on the metal-insulator transitions (MIT) in two-orbital Hubbard models by the Kotliar-Ruckenstein slave-boson approach. In the asymmetric half-filling situation, the two orbits simultaneously transit from conducting to insulating states with the increase of Coulomb correlation, accompanied by a paramagnetic (PM)-antiferromagnetic (AFM) transition. The orbital selective Mott transition found in the PM condition is completely suppressed over a wide correlation range, though it may exist in the systems away from half-filling. In the insulating state, t…
We study a bandwidth controlled Mott metal-insulator transition (MIT) between a Fermi liquid metal and a quantum spin-liquid insulator at half-filling in three dimensions (3D). Using a slave rotor approach, and incorporating gauge field fluctuations, we find a continuous MIT and discuss the finite temperature crossovers around this critical point. We show that the specific heat C=T ln ln (1/T) at the MIT and argue that the electrical transport on the metallic side near the transition should exhibit a `conductivity minimum' as a function of temperature. A possible candidate to test these predic…
We study the evolution of magnetic structure driven by a synthetic spin-orbit coupling in a one-dimensional two-component Bose-Hubbard model. In addition to the Mott insulator-superfluid transition, we found in Mott insulator phases a transition from a gapped ferromagnetic phase to a gapless chiral phase by increasing the strength of spin-orbit coupling. Further increasing the spin-orbit coupling drives a transition from the gapless chiral phase to a gapped antiferromagnetic phase. These magnetic structures persist in superfluid phases. In particular, in the chiral Mott insulator and chiral su…
