Slave-boson Theory Research Articles

Signatures of the attractive interaction in spin spectra of one-dimensional cuprate chains

Identifying the minimal model for cuprates is crucial for explaining the high-Tc pairing mechanism. Recent photoemission experiments have suggested a significant near-neighbor attractive interaction V in cuprate chains, favoring pairing instability. To determine its strength, we systematically investigate the dynamical spin structure factors S(q,ω) using the density matrix renormalization group. Our analysis quantitatively reveals a notable softening in the two-spinon continuum, particularly evident in the intense spectrum at large momentum. This softening is primarily driven by the renormalization of the superexchange interaction, as determined by a comparison with the slave-boson theory. We also demonstrate the feasibility of detecting this spectral shift in thin-film samples using resonant inelastic x-ray scattering. Therefore, this provides a distinctive fingerprint for the attractive interaction, motivating future experiments to unveil essential ingredients in cuprates. Published by the American Physical Society 2024

Charge self-consistent density functional theory plus ghost rotationally invariant slave-boson theory for correlated materials

Charge self-consistent density functional theory plus ghost rotationally invariant slave-boson theory for correlated materials

Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials

Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials

Phase coexistence in a half-filled extended Hubbard model

We analyze the coexisting ordered phases that arise in the half-filled [Formula: see text]-t-U-V extended Hubbard Model on the square lattice when tackled within the Kotliar and Ruckenstein slave boson representation in the thermodynamical limit. Particular emphasis is put on the dependence of the quasi-particle dispersions, the gaps, the spin-resolved renormalization factors, and the distribution of double occupancy on the microscopical parameters of the model. Our calculations are performed in a parameter range that is most suitable for resistive switching. In particular, the main contributions to the gaps are shown to either arise from [Formula: see text] in the weak coupling regime, or from U and V when they are the largest scales. The gaps are thus from joint spin and charge origin, and so are the order parameters.

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

We compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

Operatorial formulation of the ghost rotationally invariant slave-boson theory

We propose an operatorially exact formalism for describing the equilibrium and quantum-dynamical properties of many-electron systems interacting locally on a lattice, called ``ghost rotationally invariant slave-boson theory'' (g-RISB). We demonstrate that our theoretical framework reduces to the recently developed ghost Gutzwiller approximation (g-GA) at the mean-field level. Furthermore, we introduce the time-dependent mean-field g-RISB action, generalizing the time-dependent GA theory. Since the g-RISB is based on exact reformulation of the many-body problem, it may pave the way to the development of practical implementations for adding systematically quantum-fluctuation corrections towards the exact solution, in arbitrary dimension.

Slave-boson description of pseudogap metals in t−J models

This work discusses a modified slave-boson representation of the t-J model, which accounts for spinon-holon bound states and gives rise to a metallic pseudogap phase with sharp, Fermi-arc like features in the electron spectral function.

Charge instabilities of the extended attractive Hubbard model on the cubic lattice

The paramagnetic phase of the extended attractive Hubbard model on the cubic lattice is studied within the spin rotation invariant Kotliar-Ruckenstein slave boson representation at zero temperature. It is obtained that the quasiparticle residue of the Fermi liquid phase vanishes for all densities at an interaction strength slightly smaller than [Formula: see text] that signals the Brinkman–Rice transition, and that it weakly depends on density. While for vanishing non-local interaction parameters, homogeneous static charge instabilities are found in a rather narrow window centered around quarter filling and [Formula: see text], increasing them to [Formula: see text] results into a severe narrowing of this window. On the contrary, when all interaction parameters are attractive, for example for [Formula: see text], a large parameter range in which homogeneous static charge instabilities is found. Yet, this systematically happens inside the Fermi liquid phase.

Type-II t−J model in superconducting nickelate Nd1−xSrxNiO2

The recent observation of superconductivity at relatively high temperatures in hole doped NdNiO$_2$ has generated considerable interest, particularly due to its similarity with the infinite layer cuprates. Building on the observation that the Ni$^{2+}$ ions resulting from hole doping are commonly found in the spin-triplet state, we introduce and study a variant of the $t-J$ model in which the holes carry S=1. We name this new model the Type II $t-J$ model. We find two distinct mechanisms for $d$ wave superconductivity. In both scenarios the pairing is driven by the spin coupling $J$. However, coherence is gained in distinct ways in these two scenarios. In the first case, the spin-one holes condense leading to a $d$ wave superconductor along with spin-symmetry breaking. Different orders including spin-nematic orders are possible. This scenario is captured by a spin one slave boson theory. In the second scenario, a coherent and symmetric $d$ wave superconductor is achieved from "Kondo resonance": spin one holes contribute two electrons to form large Fermi surface together with the spin 1/2 singly occupied sites. The large Fermi surface then undergoes $d$ wave pairing because of spin coupling $J$, similar to heavy fermion superconductor. We propose a three-fermion parton theory to treat these two different scenarios in one unified framework and calculate its doping phase diagram within a self consistent mean field approximation. Our study shows that a combination of "cuprate physics" and "heavy fermion physics" may emerge in the type II $t-J$ model.

Combining Complex and Radial Slave Boson Fields within the Kotliar–Ruckenstein Representation of Correlated Impurities

AbstractThe gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle‐point approximation is performed. Within the Kotliar–Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields is presented. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.

NiRh2O4 : A spin-orbit entangled diamond-lattice paramagnet

Motivated by the interest in topological quantum paramagnets in candidate spin-$1$ magnets, we investigate the diamond lattice compound NiRh$_2$O$_4$ using {\it ab initio} theory and model Hamiltonian approaches. Our density functional study, taking into account the unquenched orbital degrees of freedom, shows stabilization of $S=1$ and $L=1$ state. We highlight the importance of spin-orbit coupling, in addition to Coulomb correlations, in driving the insulating gap, and uncover frustrating large second-neighbor exchange mediated by Ni-Rh covalency. A single-site model Hamiltonian incorporating the large tetragonal distortion is shown to give rise to a spin-orbit entangled non-magnetic ground state, largely accounting for the entropy, magnetic susceptibility, and inelastic neutron scattering results. Incorporating inter-site exchange within a slave-boson theory, we show that exchange frustration can suppress exciton condensation. We capture the dispersive gapped magnetic modes, uncover `dark states' invisible to neutrons, and make predictions for future experiments.

The electronic structure and spin-charge separation of one-dimensional SrCuO2

Based on the t-J model and slave-boson theory, we have studied the electronic structure in one-dimensional SrCuO2 by calculating the electron spectrum. Our results show that the electron spectra are mainly composed of three parts in one-dimensional SrCuO2, a sharp low-energy peak, a broad intermediate-energy peak and a high-energy peak. The sharp low-energy peak corresponds to the main band (MB) while the broad intermediate-energy peak and high-energy peak are associated with the shadow band (SB) and high-energy band (HB), respectively. From low-energy to intermediate-energy region, a clear two-peak structure (MB and SB) around the momentum [Formula: see text] appears, and the distance between two peaks decreases along the momentum direction from [Formula: see text] to [Formula: see text], then disappears at the critical momentum point [Formula: see text], leaving a single peak above [Formula: see text]. The electron spectral function in one-dimensional SrCuO2 is also the doping and temperature dependent. In particular, in the very low doping concentration, the HB merges into the MB. However, with the increases of the doping concentration, the HB separates from the MB and moves quickly to the high-binding energy region. The HB and MB are the direct results of the spin-charge separation while SB is the result of strong interaction between charge and spin parts. Therefore, our theoretical result predicts that the HB is more likely to be found at the low doping concentration, and it will be drowned in the background when the doping concentration is larger. Then with the temperature increases, the magnitude of the SB decreases, and it disappears at high temperature.

Magnetic effects on the Chern Kondo insulator

We examine the Chern Kondo insulator proposed in a square optical lattice with staggered flux induced by $s$-$p$ orbital hybridization by revisiting its realization and taking into account the magnetic effects for the Kondo phases. The Ruderman-Kittel-Kasuya-Yoshida interaction is analyzed at the weak $s$-$p$ hybridization regime, with the anisotropic magnetic effects being discussed. Furthermore, the paramagnetic and magnetic phases coexisting with Kondo couplings are systematically investigated through the slave-boson theory, for which the rich phases are obtained, including the antiferromagnetic, collinear antiferromagnetic Kondo insulator, and Kondo metal phases. The magnetic orders are shown to enhance the effective Kondo hybridization compared with the case without taking into account magnetic effects, and exhibit different influences on the bulk topology. In particular, the antiferromagnetic order always enhances the topological phase by increasing bulk gap of the Chern Kondo phases. The results show the rich topological and magnetic effects obtained in the present Chern Kondo lattice model. We also investigate how to identify the topology and strong correlation effects through measuring the Hall conductance and double occupancy, which are achievable in ultracold atom experiments.

Rigorous symmetry adaptation of multiorbital rotationally invariant slave-boson theory with application to Hund's rules physics

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 is limited to about three correlated orbitals per lattice site. We thus present a thorough symmetry-adapted advancement of RISB theory, suited to efficiently deal with multi-orbital Hubbard Hamiltonians for complete atomic-shell manifolds. It is utilized to study the intriguing problem of Hund's physics for three- and especially five-orbital manifolds on the correlated lattice, including crystal-field terms as well as spin-orbit interaction. The well-known Janus-face phenomenology, i.e. strenghtening of correlations at smaller-to-intermediate Hubbard $U$ accompanied by a shift of the Mott transition to a larger $U$ value, has a stronger signature and more involved multiplet resolution for five-orbital problems. Spin-orbit interaction effectively reduces the critical local interaction strength and weakens the Janus-face behavior. Application to the realistic challenge of Fe chalcogenides underlines the subtle interplay of the orbital degrees of freedom in these materials

Unbinding slave spins in the Anderson impurity model

We show that a generic single-orbital Anderson impurity model, lacking for instance any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridisation is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetisation of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value $R_\text{W}=2$ in the Kondo regime.

Plausible room temperature superconductivity and physical properties of cuprate superconductors based on a rigorous slave-boson representation of the t–J Hamiltonian

We present newly clarified physical properties of cuprate superconductors based on careful examinations of our earlier studies and show plausibility of room temperature superconductivity. As well known, one of the major challenging problems in high-temperature superconductivity is to reproduce the observed phase diagrams (Chatterjee, PNAS 108:9346–9349, 2011; Oda, J Phys Soc Jpn 69:983–984, 2000; Nakano, J Phys Soc Jpn 67:2622–2625, 1998; Schmidt, New J Phys 13:065014, 2011, Cyr-Choiniere (Pseudogap temperature \({T}^{*}\) of cuprate from the Nernst effect, cond-mat.supr-con, 2017; Yoshida et al. Nature 454:1072, 2008) displaying both the monotonously decreasing pseudogap temperature \(T^{*}\) and the dome-shaped superconducting transition temperature \(T_\mathrm{c}\) in the plane of temperature vs. hole concentration. Earlier we Lee et al. (Phys Rev B 64:052501–052504, 2001), Lee and Salk (Phys Rev B 71:134518, 2005), (66:054427, 2002), (J Korean Phys Soc 37:545–551, 2000) reported successful reproductions of the phase diagrams using our slave-boson theory of U(1) and SU(2) symmetry for the t–J Hamiltonian. Later we further showed that predictions (Shin and Salk, Int J Mod Phys B 29:1542003–1542011, 2015; Shin et al. J Supercond Nov Magn 23:637–640, 2010; Eom et al. Int J Mod Phys B 21:3132, 2007) of both the temperature and doping dependence of magnetic susceptibility and the universal linear scaling behavior between the magnetic resonance energy, \(E_{{\mathrm{res}}}\) and \(T_\mathrm{c}\), are consistent with inelastic neutron scattering (INS) measurements (Dai et al. Science 284:1344, 1999; He et al. Phys Rev Lett 86:1610, 2001; Bourges et al. Phys C 424:45, 2005; Stock et al. Phys Rev B 75:172510, 2007; Wakimoto et al. Phys Rev Lett 98:247003, 2007; Yu et al. Nat Phys 5:873, 2009; Isonov et al. Phys Rev B 83:214520, 2011; Keimer et al. Nature 518:179, 2015). In this work we present further clarifications of physics involved with both the phase diagrams and the INS measurements. For this cause we explore the role of spin–charge coupling on both the universal behavior of \({T^{*}}/T_\mathrm{c}\) from the phase diagrams (Chatterjee, 2011) and the universal scaling ratio of \({E_{{\mathrm{res}}}}/{k_\mathrm{B} T_\mathrm{c}}\) from the INS measurements (He et al. Phys Rev Lett 86:1610, 2001; Bourges et al. Phys C 424:45, 2005; Yu et al. Nat Phys 5:873, 2009). Both of them are found to be independent of the Heisenberg exchange coupling constant J, involving the distinctive presence of spin pairing order in association with the two energy scales, the magnetic resonance energy and the pseudogap temperature. In addition, we also discuss the J independent universal behavior of the superfluid density vs. the superconducting transition temperature. We explain most specifically physics on how all of these universal behaviors are related to the presence of spin–charge coupling. The spin–charge coupling here refers to coupling between the spin (spinon) paring order and the charge (holon) paring order which is manifested in our rigorous derivation (Lee et al. 2001; Lee and Salk, 2005, 2002) of the slave-boson-based t–J Hamiltonian. In short, we plan to explain salient physics involved with the observed universal behaviors above. Noting that in association with the universal scaling behaviors of both \({T^{*}}/T_\mathrm{c}\) and \({E_{\mathrm{res}}}/{k_\mathrm{B} T_\mathrm{c}}\) the higher the J, the higher the \(T_\mathrm{c}\), we propose that room temperature superconductivity is plausible with proper chemical synthesis of cuprate oxides meeting a suitably high J value.

Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model

The charge dynamical response function of the Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slightly affects the renormalization of the quasiparticle mass. In contrast a negative notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density we find that it enhances (reduces) the damping of the zero-sound mode. Furthermore it softens (hardens) the upper-Hubbard-band collective mode at positive (negative) doping. It is also shown that our results differ markedly from the random-phase approximation in the strong-coupling limit, even at high doping, while they compare favorably with existing quantum Monte Carlo numerical simulations.

Particle-Hole Symmetry of Charge Excitation Spectra in the Paramagnetic Phase of the Hubbard Model

The Kotliar and Ruckenstein slave-boson representation of the Hubbard model allows to obtain an approximation of the charge dynamical response function resulting from the Gaussian fluctuations around the paramagnetic saddle-point in analytical form. Numerical evaluation in the thermodynamical limit yields charge excitation spectra consisting of a continuum, a gapless collective mode with anisotropic zero-sound velocity, and a correlation induced high-frequency mode at $\omega\approx U$. In this work we show that this analytical expression obeys the particle-hole symmetry of the model on any bipartite lattice with one atom in the unit cell. Other formal aspects of the approach are also addressed.

Collective modes in the paramagnetic phase of the Hubbard model

The charge dynamical response function of the Hubbard model is investigated on the square lattice in the thermodynamic limit. The obtained charge-excitation spectra consist of a continuum, a gapless collective mode with anisotropic zero-sound velocity, and a correlation-induced high-frequency mode at $\ensuremath{\omega}\ensuremath{\approx}U$. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle point within the Kotliar and Ruckenstein slave-boson representation. Its dependence on the on-site Coulomb repulsion $U$ and density is studied in detail. An approximate analytical expression of the high-frequency mode, which holds for any lattice with one atom in the unit cell, is derived. Comparison with numerical simulations, perturbation theory, and the polarization potential theory is carried out. We also show that magnetic instabilities tend to vanish for $T\ensuremath{\gtrsim}t/6$, and finite-temperature phase diagrams are established.

Charge instabilities of the two-dimensional Hubbard model with attractive nearest neighbour interaction

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s0 are presented, whereby the positivity of F s0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t'-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U, at densities far from half filling.