Abstract We introduce a framework for characterizing many-body ground states based on the interplay of different types of concurrences. Rather than relying on a single entanglement measure, we show that the relative magnitude and scaling of spin and orbital concurrences provide a physically transparent classification of the ground state. Using the single-site Anderson model as a minimal and exactly constrained testbed, we show that spin-singlet formation and orbital superposition contribute in qualitatively different ways, leading to distinct ground-state spectral weights characterized by dominant spin or orbital degrees of freedom. Our results establish concurrences as diagnostic tools that provide a transparent characterization of the ground-state structure within this minimal setting, and suggest a possible strategy for identifying the nature of quantum superposition in more complex many-body systems.
Abstract We introduce a framework for characterizing many-body ground states based on the interplay of different types of concurrences. Rather than relying on a single entanglement measure, we show that the relative magnitude and scaling of spin and orbital concurrences provide a physically transparent classification of the ground state. Using the single-site Anderson model as a minimal and exactly constrained testbed, we show that spin-singlet formation and orbital superposition contribute in qualitatively different ways, leading to distinct ground-state spectral weights characterized by dominant spin or orbital degrees of freedom. Our results establish concurrences as diagnostic tools that provide a transparent characterization of the ground-state structure within this minimal setting, and suggest a possible strategy for identifying the nature of quantum superposition in more complex many-body systems.
We introduce a new measure of quantum entanglement, the orbital concurrence, designed to quantify orbital correlations in interacting multi-orbital electron systems. This quantity extends the concept of concurrence, originally developed for charge and spin degrees of freedom, to the orbital sector, providing a compact and physically transparent characterization of orbital entanglement. To test the validity and usefulness of this measure, we apply it to the single-site Anderson model, a paradigmatic and exactly solvable system that captures the essential interplay between localized correlated electrons and itinerant ones. In this framework, we derive exact, fully analytical expressions for the orbital concurrence and investigate its behavior in different regimes of interaction strength and hybridization. Our results demonstrate the diagnostic power of the proposed measure and open the way to its use in more complex multi-orbital impurities and lattice models.
We introduce a method for analyzing ground-state properties of quantum many-body systems, based on the characterization of separability and entanglement by single subsystem unitary operations. We apply the method to the study of the ground-state structure of several interacting spin-1/2 models, described by Hamiltonians with different degrees of symmetry. We show that the approach based on single-qubit unitary operations allows us to introduce ``entanglement excitation energies,'' a set of observables that can characterize ground-state properties, including the quantification of single-site entanglement and the determination of quantum critical points. The formalism allows us to identify the existence and location of factorization points, and a purely quantum ``transition of entanglement'' that occurs at the approach of factorization. This kind of quantum transition is characterized by a diverging ratio of excitation energies associated with single-qubit unitary operations.
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants, we demonstrate that our real-space OPs provide a more refined classification. In the extended Su-Schrieffer-Heeger model, we show that the standard winding number is insufficient to fully distinguish all phases; our OPs reveal a hidden sub-structure where each topological sector splits into two distinct phases. Beyond identifying the phase boundaries, these OPs quantify the depth of a phase, and remain robust in characterizing transitions in disordered systems. Furthermore, our approach provides a practical finite-size diagnostic for the Berezinskii-Kosterlitz-Thouless transition in the interacting spin-1/2 XXZ model. The presented framework offers a broadly applicable tool for uncovering the phase diagrams of diverse interacting and non-interacting quantum many-body systems.
Abstract Frustration of classical many-body systems can be used to distinguish ferromagnetic interactions from anti-ferromagnetic ones via the Toulouse conditions. A quantum version of the Toulouse conditions provides a similar classification based on the local ground states. We compute the global ground states for a family of models with Heisenberg-like interactions and analyse their behaviour with respect to frustration, entanglement and degeneracy. For that we develop analytical and numerical analysing tools capable of quantifying the interplay between those three quantities. We find that the quantum Toulouse conditions provide a proper classification, however, refinements can be found. Our results show how the different local ground states affect the interplay and pave the way for further generalisation and possible applications to other quantum many-body systems.
The concept of entanglement in many‑body physics has traditionally focused on spin or particle‑number degrees of freedom. Here we introduce a novel class of fermionic quantum phases in which orbital degrees of freedom of identical particles become entangled across spatially distinct sites. We construct the general form of the many‑body wavefunction for a system of N fermions occupying L orbitals per site, and show that the ground state of certain interacting Hamiltonians can be written as |\Psi> = \sum_{i,j} c_{ij} | \phi_i \phi_j >, where | \phi_i > and | \phi_j > denote single‑particle orbital states localized at different lattice sites. This entangled orbital structure leads to emergent properties distinct from conventional band insulators, Mott insulators, or spin liquids. We discuss the symmetry constraints, the role of fermionic statistics, and the topological aspects that arise when the orbital entanglement is global. Theoretical analysis predicts that FOEPs can host protected edge modes, exotic quasiparticles, and non‑Abelian statistics in two‑dimensional lattices. We also outline experimental signatures that could be observed in engineered cold‑atom systems, photonic lattices, or layered transition‑metal dichalcogenides, and argue that the discovery of FOEPs would open a new frontier in the search for quantum materials with high‑temperature superconductivity or quantum information processing capabilities.
The von Neumann entanglement entropy of exact valence-bond ground states is studied in two frustrated one-dimensional spin chains: the spin-1/2 Majumdar-Ghosh (MG) model and the spin-3/2 J1-J2-J3 chain in its fully dimerized (FD) and partially dimerized (PD) phases. Using matrix-product-state representations, the entropy is computed as a function of system size for three complementary bipartitions - half-chain, single-site, and pairwise - under both open and periodic boundary conditions. In all cases, the entropy saturates to a finite constant in the thermodynamic limit, confirming area-law behavior. The saturation values, extracted via finite-size scaling, are directly related to the underlying virtual-spin bond structure. The MG model and FD phase exhibit similar entanglement behavior, differing primarily in saturation magnitude determined by spin value and bond multiplicity, and both display even-odd oscillations and exponential convergence with system size. In contrast, the PD phase shows qualitatively distinct signatures, including multiple half-chain saturation values depending on the bond type at the cut, asymmetric edge contributions in the single-site entropy, and a multi-band structure in the pairwise entropy reflecting the coexistence of single- and double-singlet bonds. These results establish entanglement entropy as a robust signature of frustrated bond architecture, enabling clear distinction among dimerized phases with different spin magnitude, bond multiplicity, and dimerization patterns.