Symmetry-resolved quasilocal entanglement as a key to Mott and pseudogap physics in plaquette CDMFT

Abstract

In order to identify intrinsic quantum resources in strongly interacting fermionic systems, we introduce a symmetry resolution of the parity-superselected two-site entanglement, as measured by both the fermionic negativity and the relative entropy of entanglement. We discuss how the symmetry resolution can be extended also to the full entanglement in pure and mixed two-site states. We apply our recipe to the Hubbard model, first for a dimer, and then for a plaquette cluster dynamical mean-field theory, an established method tailored to accurately capture short-range correlations. Following the evolution of the model through the interaction- and density-driven Mott transitions at zero temperature, we highlight how the three symmetry-resolved components of the two-site entanglement probe different key aspects of Mott and pseudogap physics.

The paper asks whether two-site entanglement can distinguish the short-range quantum correlations associated with Mott localization and pseudogap physics from those generated by single-particle hopping. It develops a decomposition into spin-singlet, holon–doublon and hopping contributions, using fermionic logarithmic negativity and relative entropy of entanglement (REE). For pure, charge-conserving two-site states, the three contributions correspond to local charge-jump sectors of the fermionic partial transpose. For mixed states, only the spin-singlet and holon–doublon sectors remain rigorously separated after imposing local parity superselection; the hopping contribution is defined through the difference in trace-norm excess between full and superselected negativities. Small-sector PPT criteria detect superselected separability exactly, while existing closed REE formulas apply under additional symmetries. Analytical checks treat an isolated Hubbard dimer and nearest neighbors in a noninteracting square lattice, where both superselected contributions vanish. Applications use zero-temperature, paramagnetic $2\times2$ plaquette CDMFT with an exact-diagonalization impurity solver. At half filling, the Mott transition occurs near $U=1.55D$, with $D=4t$; spin-singlet REE approaches approximately $0.19$ bits at strong coupling, while holon–doublon entanglement concentrates near the transition. At $U=2.3D$, spin-singlet entanglement persists into the doped pseudogap-like metal but vanishes across its first-order transition to an overdoped metal; holon–doublon entanglement retains a small tail. Limitations include finite-cluster and finite-bath effects, demonstrated weak-coupling CDMFT artifacts, inaccessible full mixed-state REE, and unresolved generalization to symmetry-broken phases. The order of the metal–metal transition may change beyond plaquette CDMFT.