Slave-boson Mean-field Theory Research Articles

Solving local constraint condition problem in slave particle theory with the BRST quantization

With the Becchi–Rouet–Stora–Tyutin (BRST) quantization of gauge theory, we solve the long-standing difficult problem of the local constraint conditions, i.e. the single occupation of a slave particle per site, in the slave particle theory. This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ i which ensures the constraint: in the Hamiltonian formalism of the theory, λ i is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism, λ i (t) becomes time-dependent and plays a role of gauge field. This implies that the redundant degrees of freedom of λ i (t) are introduced and must be removed by the additional constraint, the gauge fixing condition (GFC) ∂ t λ i (t) = 0. In literature, this GFC was missed. We add this GFC and use the BRST quantization of gauge theory for Dirac’s first-class constraints in the slave particle theory. This GFC endows λ i (t) with dynamics and leads to important physical results. As an example, we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal, which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field (MF) theory. For the t–J model, we find that the dynamic effect of λ i (t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K. The renormalized T c is then close to that in cuprates.

Mottness in two-dimensional van der Waals Nb3X8 monolayers (X=Cl,Br,andI)

We investigate strong electron-electron correlation effects on two-dimensional van der Waals materials ${\mathrm{Nb}}_{3}{X}_{8} (X=\mathrm{Cl},\mathrm{Br},\phantom{\rule{0.28em}{0ex}}\text{and}\phantom{\rule{0.28em}{0ex}}\mathrm{I})$. We find that the monolayers ${\mathrm{Nb}}_{3}{X}_{8}$ are ideal systems close to the strong correlation limit. They can be described by a half-filled single band Hubbard model in which the ratio between the Hubbard, $U$, and the bandwidth, $W, U/W\ensuremath{\approx}5--10$. Both Mott and magnetic transitions of the material are calculated by the slave boson mean-field theory. Doping the Mott state, a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ superconducting pairing instability is found. We also construct a tunable bilayer Hubbard system for two sliding ${\mathrm{Nb}}_{3}{X}_{8}$ layers. The bilayer system displays a crossover between the band insulator and Mott insulator.

Antiferromagnetism and chiral-[formula omitted] wave superconductivity in a honeycomb lattice close to Mott state

The antiferromagnetism (AFM) and chiral-d wave superconductivity (SC) in a honeycomb lattice close to an antiferromagnetic (AF) Mott state at half band filling are studied with a t−J model and slave boson mean field theory. The order parameters and single particle dispersion relations at different band filling fractions are investigated. It is found that the AFM enhances the SC, and leads to nodal single particle dispersion relations at two band filling fractions. These unexpected nodal dispersion relations out of nodeless chiral-d wave superconducting order are discussed. A comparison between AF chiral-d wave states and AF extended-s wave states is also given to highlight the pertinent features in chiral-d wave superconducting states. This study may be related to the honeycomb lattice materials such as the In3Cu2VO9 compound.

Correlation of Yu-Shiba-Rusinov States and Kondo Resonances in Artificial Spin Arrays on an s-Wave Superconductor.

Mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to their potential for the realization of topological superconductivity. Individual magnetic impurities produce states within the superconducting energy gap known as Yu–Shiba–Rusinov (YSR) states. Here, using the tip of a scanning tunneling microscope, we artificially craft spin arrays consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms (IFA) on a superconducting oxygen-reconstructed Ta(100) surface and show that the magnetic interaction between the adatom and the IFA assembly can be tuned by adjusting the number of IFAs in the assembly. The YSR state experiences a characteristic crossover in its energetic position and particle–hole spectral weight asymmetry when the Kondo resonance shows spectral depletion around the Fermi energy. By the help of slave-boson mean-field theory (SBMFT) and numerical renormalization group (NRG) calculations we associate the crossover with the transition from decoupled Kondo singlets to an antiferromagnetic ground state of the Fe adatom spin and the IFA assembly effective spin.

Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large- z limit

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 the closing of the charge gap at a critical value of the Hubbard $U_c$ and the corresponding doublon density $n_d^c$, hopping $\chi_d^c$ and doublon-holon pairing $\Delta_d^c$ amplitudes. We find $U_c=U_{\rm BR} [1 -2n_d^c -\sqrt{z} (\chi_d^c +\Delta_d^c))] \simeq0.8U_{\rm BR}$, where $U_{\rm BR}$ is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a $U(1)$ quantum spin liquid with nonzero intersite spinon hopping that survives the large-$z$ limit and lifts the $2^N$-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact $U(1)$ gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.

Insulator-metal transition and quasi-flat-band of Shastry–Sutherland lattice

Insulator-metal transition is investigated self-consistently on the frustrated Shastry–Sutherland lattice in the framework of Slave-Boson mean-field theory. Due to the presence of quasi-flat band structure characteristic, the system displays a spin-density-wave (SDW) insulating phase at the weak doping levels, which is robust against frustration, and it will be transited into an SDW metallic phase at high doping levels. As further increasing the doping, the temperature or the frustration on the diagonal linking bonds, the magnetic order m will be monotonically suppressed, resulting in the appearance of a paramagnetic metallic phase. Although the Fermi surface of the SDW metallic phase may be immersed by temperature, the number of mobile charges is robust against temperature at weak doping levels.

Numerical investigation of spin excitations in a doped spin chain

We study the doping evolution of spin excitations in a 1D Hubbard model and its downfolded spin Hamiltonians, by using exact diagonalization combined with cluster perturbation theory. In all models, we observe hardening (softening) of spin excitations upon electron (hole) doping, which are reminiscent of recent experiments on 2D cuprate materials. We also find that the 3-site and even higher-order terms are crucial for the low-energy effective spin models to reproduce the magnetic spectra of doped Hubbard systems at a quantitative level. To interpret the numerical results, we further employ a strong coupling slave-boson mean-field theory. The mean-field theory provides an intuitive understanding of the overall compact support of dynamic spin structure factors, including the shift of zero-energy modes and change of spin excitation bandwidth with doping. Our results can serve as predictive benchmarks for future inelastic x-ray or neutron scattering experiments on doped 1D antiferromagnetic Mott insulators.

Rotationally invariant slave-boson and density matrix embedding theory: Unified framework and comparative study on the one-dimensional and two-dimensional Hubbard model

We present detailed benchmark ground-state calculations of the one- and two-dimensional Hubbard model utilizing the cluster extensions of the rotationally invariant slave-boson (RISB) mean-field theory and the density matrix embedding theory (DMET). Our analysis shows that the overall accuracy and the performance of these two methods are very similar. Furthermore, we propose a unified computational framework that allows us to implement both of these techniques on the same footing. This provides us with a new line of interpretation and paves the ways for developing systematically new generalizations of these complementary approaches.

Interplay between chiral magnetic and Kondo effects in Weyl metal phase

We investigate the Kondo effect in a Weyl metal state, which occurs from a spin-orbit coupled Dirac metal phase under magnetic fields. We start from an effective field theory in terms of low-energy fermions on a pair of chiral Fermi surfaces, which takes into account both the Berry curvature and chiral anomaly. Resorting to the U(1) slave-boson mean-field theory, we find that the effective Kondo temperature increases monotonically as a function of the external magnetic field due to enhancement of the density of states. The enhancement is originated from the chiral magnetic effect which is novel feature of Weyl metals. This leads to the prediction of the magnetic-field dependence in the logarithmic temperature dependence of the longitudinal magnetoconductivity.

Quantum phase transition in a realistic double-quantum-dot system

Observing quantum phase transitions in mesoscopic systems is a daunting task, thwarted by the difficulty of experimentally varying the magnetic interactions, the typical driving force behind these phase transitions. Here we demonstrate that in realistic coupled double-dot systems, the level energy difference between the two dots, which can be easily tuned experimentally, can drive the system through a phase transition, when its value crosses the difference between the intra- and inter-dot Coulomb repulsion. Using the numerical renormalization group and the semi-analytic slave-boson mean-field theory, we study the nature of this phase transition, and demonstrate, by mapping the Hamiltonian into an even-odd basis, that indeed the competition between the dot level energy difference and the difference in repulsion energies governs the sign and magnitude of the effective magnetic interaction. The observational consequences of this transition are discussed.

Heat current through an artificial Kondo impurity beyond linear response

We investigate the heat current of a strongly interacting quantum dot in the presence of a voltage bias in the Kondo regime. Using the slave-boson mean-field theory, we discuss the behavior of the energy flow and the Joule heating. We find that both contributions to the heat current display interesting symmetry properties under reversal of the applied dc bias. We show that the symmetries arise from the behavior of the dot transmission function. Importantly, the transmission probability is a function of both energy and voltage. This allows us to analyze the heat current in the nonlinear regime of transport. We observe that nonlinearities appear already for voltages smaller than the Kondo temperature. Finally, we suggest to use the contact and electric symmetry coefficients as a way to measure pure energy currents.

Fate of the spin- 12 Kondo effect in the presence of temperature gradients

We consider a strongly interacting quantum dot connected to two leads held at quite different temperatures. Our aim is to study the behavior of the Kondo effect in the presence of large thermal biases. We use three different approaches, namely, a perturbation formalism based on the Kondo Hamiltonian, a slave-boson mean-field theory for the Anderson model at large charging energies and a truncated equation-of-motion approach beyond the Hartree-Fock approximation. The two former formalisms yield a suppression of the Kondo peak for thermal gradients above the Kondo temperature, showing a remarkably good agreement despite their different ranges of validity. The third technique allows us to analyze the full density of states within a wide range of energies. Additionally, we have investigated the quantum transport properties (electric current and thermocurrent) beyond linear response. In the voltage-driven case, we reproduce the split differential conductance due to the presence of different electrochemical potentials. In the temperature-driven case, we observe a strongly nonlinear thermocurrent as a function of the applied thermal gradient. Depending on the parameters, we can find nontrivial zeros in the electric current for finite values of the temperature bias. Importantly, these thermocurrent zeros yield direct access to the system's characteristic energy scales (Kondo temperature and charging energy).

Possible three-dimensional superconducting properties of strongly correlated honeycomb compound In3Cu2VO9

We present the zero- and finite-temperature superconducting properties of a modified t − J − Jc model on three-dimensional honeycomb lattice by employing the strongly correlated Slave Boson mean-field theory, focusing on the low energy physics in In3Cu2VO9. We find that the highest superconducting transition temperature Tc ≈ 4 K occurs at doping hole concentration δ = 0.03. The superconducting phase disappears at doping concentration of δ = 0.06. The superconducting ground state in doped In3Cu2VO9 supports a dx2−y2 + idxy pairing symmetry when the interlayer coupling Jc increases from 1.2 to 5.2 meV. Our theoretical results suggest that doped In3Cu2VO9 is a possible superconducting honeycomb system.

Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films.

We theoretically study the magnetic properties of pyrochlore iridate bilayer and trilayer thin films grown along the [111] direction using a strong coupling approach. We find the ground state magnetic configurations on a mean field level and carry out a spin-wave analysis about them. In the trilayer case the ground state is found to be the all-in-all-out (AIAO) state, whereas the bilayer has a deformed AIAO state. For all parameters of the spin-orbit coupled Hamiltonian we study, the lowest magnon band in the trilayer case has a nonzero Chern number. In the bilayer case we also find a parameter range with nonzero Chern numbers. We calculate the magnon Hall response for both geometries, finding a striking sign change as a function of temperature. Using a slave-boson mean-field theory we study the doping of the trilayer system and discover an unconventional time-reversal symmetry broken d+id superconducting state. Our study complements prior work in the weak coupling limit and suggests that the [111] grown thin film pyrochlore iridates are a promising candidate for topological properties and unconventional orders.

Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions

Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.

Signatures of strong correlation effects in resonant inelastic x-ray scattering studies on cuprates

Recently, spin excitations in doped cuprates are measured using the resonant inelastic X-ray scattering (RIXS). The paramagnon dispersions show the large hardening effect in the electron-doped systems and seemingly doping-independence in the hole-doped systems, with the energy scales comparable to that of the antiferromagnetic magnons. This anomalous hardening effect was partially explained by using the strong coupling t-J model but with a three-site term(Nature communications 5, 3314 (2014)). However we show that hardening effect is a signature of strong coupling physics even without including this extra term. By considering the t-t'-t"-J model and using the Slave-Boson (SB) mean field theory, we obtain, via the spin-spin susceptibility, the spin excitations in qualitative agreement with the experiments. These anomalies is mainly due to the doping-dependent bandwidth. We further discuss the interplay between particle-hole-like and paramagnon-like excitations in the RIXS measurements.

Phase lamination in a t–J bilayer at finite temperature

A bilayered t–J model is investigated with a slave boson mean field theory. A spontaneous phase lamination (PL) into a layer dominated by antiferromagnetism (AFM) and a layer dominated by superconductivity (SC) is found at a low doping density and low temperature regime. Raising the temperature removes the PL and SC, turns the system into a homogeneously antiferromagnetic (AF) bilayer, and eventually a homogeneously paramagnetic bilayer at high temperature. The PL circumvents the competition between AFM and SC, and may result in a higher superconducting transition temperature. The density of states of low energy single particle excitation in the homogeneously AF state at intermediate temperature is reduced by the AF scattering. The relation between this study and the bilayered superconducting cuprates is discussed.

Low-energy model and electron-hole doping asymmetry of single-layer Ruddlesden-Popper iridates

We study the correlated electronic structure of single-layer iridates based on structurally-undistorted Ba$_2$IrO$_4$. Starting from the first-principles band structure, the interplay between local Coulomb interactions and spin-orbit coupling is investigated by means of rotational-invariant slave-boson mean-field theory. The evolution from a three-band description towards an anisotropic one-band ($J=1/2$) picture is traced. Single-site and cluster self-energies are used to shed light on competing Slater- and Mott-dominated correlation regimes. We reveal a clear asymmetry between electron and hole doping, notably in the nodal/anti-nodal Fermi-surface dichotomy at strong coupling. Electron-doped iridates appear comparable to hole-doped cuprates due to the different sign of the next-nearest-neighbor hopping $t'$.

Coexistence of antiferromagnetism and superconductivity of [formula omitted] model on honeycomb lattice

Motivated by recent experimental study of antiferromagnetic property of honeycomb compound In3Cu2VO9 [Yan et al. (2012)], we explore possible superconductivity and its coexistence with collinear antiferromagnetism. Explicitly, we use the t-t′-J model on the honeycomb lattice as our starting point and employ the slave-boson mean-field theory. In the antiferromagnetic normal state, the characteristic doping evolution of Fermi surface shows that only one effective singe band is active, which suggests that the potential pairing symmetry is more likely the time-reversal symmetry breaking d+id, rather than the extended s-wave pairing structure. It is found that this superconducting state coexists with the antiferromagnetism in a broad doping regime, which is consistent with the numerical calculations. The local density of states and its thermodynamic property of the superconducting state has been studied in detail with an effective single-band picture for understanding other physical observable such as superfluid density. The present work may be useful in experimentally exploring possible superconductivity of this kind of materials on the honeycomb lattice and contributes to the understanding of the unconventional superconductivity on general two-dimensional correlated electron systems.

X-boson cumulant approach to the topological Kondo insulators

In this work we present a generalization of our previous work of the X-boson approach to the periodic Anderson model (PAM), adequate to study a novel class of intermetallic 4f and 5f orbitals materials: the topological Kondo insulators, whose paradigmatic material is the compound SmB6.For simplicity, we consider a version of the PAM on a 2D square lattice, adequate to describe Ce-based compounds in two dimensions. The starting point of the model is the 4f - Ce ions orbitals, with J = 5/2 multiplet, in the presence of spin-orbit coupling. Our technique works well for all of the parameters of the model and avoids the unwanted phase transitions of the slave boson mean field theory. We present a critical comparison of our results with those of the usual slave boson method, that has been intensively used to describe this class of materials. We also obtain a new valence first order transition which we attribute to the k⃗ dependence of the hybridization.