Abstract
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.
Highlights
The idea of utilizing subsidiary degrees of freedom for modeling the strong interactions in many-electron systems has a long history in condensed-matter physics [1], and it is nowadays imbued within numerous theoretical frameworks, such as tensor-network methods [2,3], neural-network quantum states [4], slave-boson methods [5,6,7,8,9,10,11,12], and the recently developed ghost Gutzwiller approximation (g-GA) [13,14,15]
We derived a ground-state and time-dependent theory of multiorbital electronic systems interacting locally on a lattice, which reduces to the g-GA at the mean-field level
This provides an alternative perspective on the g-GA theory, which may pave the way for developing new generalizations
Summary
The idea of utilizing subsidiary degrees of freedom for modeling the strong interactions in many-electron systems has a long history in condensed-matter physics [1], and it is nowadays imbued within numerous theoretical frameworks, such as tensor-network methods [2,3], neural-network quantum states [4], slave-boson methods [5,6,7,8,9,10,11,12], and the recently developed ghost Gutzwiller approximation (g-GA) [13,14,15]. Its current formulation (that is based on extending the Gutzwiller wave function, rather than a slave-boson perspective) does not provide tools for including systematic corrections towards the exact solution in low-dimensional systems (such as those necessary for capturing the nonlocal correlation effects) Another way of improving the accuracy of the RISB mean-field solution is to take into account perturbatively the quantum-fluctuation corrections. Since the g-RISB mean-field solution (i.e., the g-GA) describes the electronic structure in terms of emergent Bloch excitations [13], and such description proved to have accuracy comparable with DMFT in all parameter regimes [13,14] (including the Mott phase), our formalism may pave the way to implementations able to take into account perturbatively the residual effective interactions between such generalized emergent states, allowing us to perform high-precision calculations of strongly correlated electron systems, in arbitrary dimension
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