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arXiv:2609.24315

Slave-Rotor and Auxiliary Chain Analysis of the Mott Transition in a Modified Periodic Anderson Model

A. Majumder, Sudeshna Sen

Published Sep 21, 2026• 0 citations
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Abstract

The Mott-Hubbard transition is a paradigmatic phenomenon driven by strong electronic correlations. We investigate this transition in a three-orbital modified periodic Anderson model using slave-rotor mean-field theory. A minimal two-site cluster extension is introduced to understand the minimal effects of short-range spatial correlations. In comparison to the single-site solution, short-range spatial correlations reveal a shift of the transition point. Going beyond the slave-rotor analysis, we also evaluate the dynamical self-energy and map it onto the boundary Green's function of a non-interacting semi-infinite auxiliary chain. For the metallic phase, the resulting hopping pattern corresponds to a topologically trivial generalized Su--Schrieffer--Heeger chain. This construction provides a framework for exploring the possible topological character of the Mott transition in this model.

DOI
10.48550/arxiv.2609.24315

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The Mott-Hubbard transition is a paradigmatic phenomenon driven by strong electronic correlations. We investigate this transition in a three-orbital modified periodic Anderson model using slave-rotor mean-field theory. A minimal two-site cluster extension is introduced to understand the minimal effects of short-range spatial correlations. In comparison to the single-site solution, short-range spatial correlations reveal a shift of the transition point. Going beyond the slave-rotor analysis, we also evaluate the dynamical self-energy and map it onto the boundary Green's function of a non-interacting semi-infinite auxiliary chain. For the metallic phase, the resulting hopping pattern corresponds to a topologically trivial generalized Su--Schrieffer--Heeger chain. This construction provides a framework for exploring the possible topological character of the Mott transition in this model.
Abstract The Mott transition is a paradigmatic phenomenon where Coulomb interactions between electrons drive a metal‐insulator phase transition. It is extensively studied within the Hubbard model, where a quantum critical transition occurs at a finite temperature second‐order critical point. This work investigates the Mott transition in a modified periodic Anderson model that may be viewed as a three‐orbital lattice model including an interacting, localized orbital coupled to a delocalized conduction orbital via a second conduction orbital. Within the dynamical mean field theory, this model possesses a strictly zero temperature quantum critical point separating a Fermi liquid and a Mott insulating phase. By employing a simplified version of the dynamical mean field theory, namely, the two‐site or linearized dynamical mean field theory, an analytical estimate is provided for the critical parameter strengths at which the transition occurs at zero temperature. An analytical estimate of the single‐site von Neumann entanglement entropy is also provided. This measure can be used as a robust identifier for the phase transition. These calculations are extended to their cluster version to incorporate short‐range, spatial correlations and discuss their effects on the transition observed in this model.
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 range charge correlator in the Mott insulating state. It predicts a continuous Mott transition with non-divergent quasiparticle mass at the transition point. We also show that the commonly used on-site mean field decoupling for the slave rotor corresponds to the Gutzwiller approximation for the Gutzwiller projected wave function with only on-site charge correlator, which can not describe the Mott transition in any finite dimensional system.
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 into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal-insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi-liquid coherence scale and the Mott gap, found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.
The periodic Anderson model (PAM) is studied within the framework of dynamical mean-field theory, with particular emphasis on the interaction-driven Mott transition it contains, and on resultant Mott insulators of both Mott-Hubbard and charge-transfer type. The form of the PAM phase diagram is first deduced on general grounds using two exact results, over the full range of model parameters and including metallic, Mott, Kondo and band insulator phases. The effective low-energy model which describes the PAM in the vicinity of a Mott transition is then shown to be a one-band Hubbard model, with effective hoppings that are not in general solely nearest neighbour, but decay exponentially with distance. This mapping is shown to have a range of implications for the physics of the problem, from phase boundaries to single-particle dynamics; all of which are confirmed and supplemented by NRG calculations. Finally we consider the locally degenerate, non-Fermi liquid Mott insulator, to describe which requires a two-self-energy description. This is shown to yield a number of exact results for the associated local moment, charge, and interaction-renormalised levels, together with a generalisation of Luttinger's theorem to the Mott insulator.
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 Uc 3t1U_c ~ 3 t_1Uc​ 3t1​. Several aspects of the slave spin method, its gauge theory and various possible mean-field states associated with this approach have been discussed.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.