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arXiv:2610.08575

Ghost rotationally invariant slave-boson approach to response functions

Tsung-Han Lee, Corey Melnick, Nicola Lanatà, Gabriel Kotliar

Published Oct 6, 2026• 0 citations
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Abstract

We propose a finite-temperature Gaussian-fluctuation formalism for response functions within ghost rotationally invariant slave-boson (gRISB) theory and apply it to the two-dimensional Hubbard model. The gRISB magnetic phase boundary and static spin and charge susceptibilities capture the trends of dynamical mean-field theory (DMFT), significantly improving upon standard RISB and the random phase approximation (RPA). At the RISB level, our formalism recovers the Kotliar-Ruckenstein response. The dynamical susceptibilities resolve paramagnons, low-energy sound modes, and high-energy Hubbard excitations. Because they are evaluated directly on the real-frequency axis, the results avoid Matsubara truncation, stochastic sampling, and numerical analytic continuation. We also introduce a conserving quasiparticle approximation that expresses the response in terms of dressed Green's functions and vertex corrections.

DOI
10.48550/arxiv.2610.08575

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We propose a finite-temperature Gaussian-fluctuation formalism for response functions within ghost rotationally invariant slave-boson (gRISB) theory and apply it to the two-dimensional Hubbard model. The gRISB magnetic phase boundary and static spin and charge susceptibilities capture the trends of dynamical mean-field theory (DMFT), significantly improving upon standard RISB and the random phase approximation (RPA). At the RISB level, our formalism recovers the Kotliar-Ruckenstein response. The dynamical susceptibilities resolve paramagnons, low-energy sound modes, and high-energy Hubbard excitations. Because they are evaluated directly on the real-frequency axis, the results avoid Matsubara truncation, stochastic sampling, and numerical analytic continuation. We also introduce a conserving quasiparticle approximation that expresses the response in terms of dressed Green's functions and vertex corrections.
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We assess the accuracy of ghost-rotationally-invariant slave-boson (g-RISB) theory in multiorbital systems by applying it to both the three-orbital degenerate Hubbard model and a realistic Sr2RuO4{\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}Sr2​RuO4​ model extracted from first-principle simulations and comparing the results to those obtained using dynamical mean-field theory (DMFT). Our findings indicate that g-RISB's accuracy can be systematically improved toward the exact DMFT limit in infinite-dimensional multiorbital models by increasing the number of ghost orbitals. This allows for a more precise description of aspects of Hund metal physics and Mott physics compared with the original RISB approach. We also demonstrate that g-RISB reliably captures the quasiparticle weights, Fermi surface, and low-energy spectral function for the realistic Sr2RuO4{\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}Sr2​RuO4​ model compared with DMFT. Moreover, we showcase the potential of using the density matrix renormalization group method as an impurity solver within the g-RISB framework to study systems with a larger number of ghost orbitals. These results show the potential of g-RISB as a reliable tool for simulating correlated materials. The connection between the g-RISB and DMFT self-energy is also discussed.
We develop a generalization of the ghost-rotationally-invariant slave-boson (ghost-RISB) method that incorporates local phonon modes coupled to arbitrary on-site electronic degrees of freedom, enabling a nonperturbative treatment of electron-electron and electron-phonon interactions within an efficient variational framework. The method extends the ghost-orbital construction to capture dynamical self-energy effects and phonon-induced renormalizations beyond static slave-boson approaches. Benchmarking against dynamical mean-field theory (DMFT) results for the Hubbard-Holstein model, we find excellent quantitative agreement for electron quasiparticle weights and phonon properties across a wide range of coupling strengths, and it captures accurately the competition between electron-electron and electron-phonon interactions. We show that the inclusion of the ghost orbitals is crucial to accurately describe the regime of low-frequency, strongly dynamical, phonons. The extended ghost-RISB achieves this accuracy at a fraction of the computational cost of DMFT, due to its self-consistency rooted in static observables instead of dynamical ones, enabling rapid exploration of correlated electron-phonon phase diagrams. We exploit this advantage to characterize the most demanding regime of strong coupling and adiabatic phonons. Our analysis shows a suppression of the superconducting order parameter, which is interpreted as a Franck-Condon-like reduction of the overlap between the phonon wavefunctions associated with empty and doubly-occupied sites in the bipolaronic regime.
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.
We determine the free energy of strongly correlated electron systems in the example of the Hubbard model by calculating the contribution of spin and charge fluctuations to the Gutzwiller approximation mean-field result. We employ the slave-boson formulation of Kotliar and Ruckenstein in its spin-rotation-invariant form in the usual continuous-time approximation of the functional integral representation, corrected by “high-frequency contributions” ( SRIKR + ). In contrast to all previous attempts to calculate the fluctuation contribution to the free energy within the spin-rotation-invariant Kotliar-Ruckenstein slave-boson representation (SRIKR) scheme our result preserves the noninteracting limit. We show that the correct form of the kinetic energy renormalization is essential. The results for the ground-state energy in the paramagnetic phase are in very good agreement with state-of-the-art results obtained by methods such as density matrix embedding theory, quantum Monte Carlo, and others. The leading low-temperature behavior of the free energy allows us to extract the quasiparticle effective mass, in particular its enhancement near a continuous phase transition into an ordered state. Our work demonstrates that the SRIKR + method is competitive with the best available alternative methods and equips the slave-boson approach with an improved synoptic power to explore strongly correlated electron systems.