Faithful entanglement description of strongly correlated materials

• To appear soon: resolution of a quantum information conundrum regarding the Mott metal-insulator transition in the 2d Hubbard model (arXiv preprint){open code for reproducibility}
  
  > Among the most debated topics in condensed matter physics, the Mott-Hubbard transition has recently seen a renovated bloom of original interpretations: from a local mapping to an amazingly simple symmetry-protected topological phase transition in the infinite coordination limit [1], to information-theoretical characterizations through the single-site von Neumann entropy and mutual information [2,3,4], capturing the entanglement and classical correlations at all length-scales that can be simulated by the theory or cold-atom experiment. We embrace an intermediate approach by evaluating, within CDMFT/ED (exact diagonalization based cluster dynamical mean-field theory), local and quasilocal reduced density matrices, from a single site up to the entire simulated clusters. Amazingly, all the von Neumann entropies of these quasilocal density matrices, share the same qualitative behavior: a monotonic damping with increasing interaction values. The result holds the comparison with recent seminal work [5] devising a non-equilibrium extension of inhomogeneous dynamical mean-field theory, able to target the second Renyi entropy and mutual information for subsystems up to 128 sites in the square lattice. Hence, von Neumann or generalized Renyi entropies, from single sites up to mesoscopic chunks of lattice, all describe the Mott metal-insulator transition as a gradual decrease of quantum correlations. But isn't the Mott insulator the paradigm of strongly correlated electronic quantum states? Well, we found that the spatially resolved entanglement between two orbitals, without any contribution from the rest of the lattice, recovers the inherent character of strongly correlated insulators. As demonstrated through suitable upper and lower bound to their magnitude, both quantum and classical correlations abruptly increase at the Mott transition, while being quickly damped with inter-site distance, at all interaction values. This suggests that Mott localization might be dominated by a concept of genuine quasilocal entanglement, supporting the relevance of the infinite coordination picture introduced in [1], as a seminal fully local approximation, while somewhat undermining the expectations for long-range entanglement topological order and quantum spin liquid behavior, often found in literature.
   
• Currently working on:  Two-orbital entanglement description of the doping-driven insulator-to-metal transition and entanglement properties of the intermediate pseudogap phase.
  
  > Doping a Mott insulator with holes charge transport is immediately recovered. But not by a direct transition to the weakly correlated Fermi liquid state. Away from half filling the Mott insulator and the normal metal are always separated by an intermediate exotic conducting phase, known as pseudogap metal. Little is known about its physical nature and we aim are eager to discover what the two-orbital entanglement [see above] could reveal on the matter. Stay tuned!
   
• Currently working on: Two-orbital entanglement description of correlated topological phase transitions
  
  > Recent research pursued by collaborators from the CNR-IOM group [1] has shown how symmetry protected topological phase transitions can drastically change character when strong correlations come into play. The role of local (inter-orbital) versus nonlocal (inter-atomic) correlation has been so far studied indirectly, by looking at the structure of the self-energy matrix, within a minimal cluster dynamical mean-field description [2]. We aim to target the issue more directly, from a quantum information perspective, by means of the recently introduced two-orbital entanglement description of strongly correlated materials [see above].

Magnetism and topology of strongly-correlated Dirac fermions.

• In preparation: Nontrivial competition between in- / out-of-plane magnetic order and topology in the Kane-Mele-Hubbard model. {open code for reproducibility}
  
  > While the regular Hubbard model on the honeycomb lattice has full SU(2) spin symmetry, thus featuring an isotropic semimetal-to-antiferromagnet transition at the increase of electron-electron interactions, the topological spin-orbit coupling introduced by Kane and Mele in 2005 brings in nontrivial frustration effects. The competition between the nearest-neighbor and next-nearest-neighbor magnetic terms resolves —in the thermodynamic limit— into an effective suppression of the out-of-plane antiferromagnetic order. While the overall picture has been essentially confirmed by most suitable numerical methods, many details are still debated, due to hazy, subtle effects of size scaling.  Most notably, early hints at an intermediate quantum spin liquid phase, sandwiched between the topological and the magnetic insulator, have been disputed by extreme-scale quantum Montecarlo simulations, carried out by renowned SISSA professor Sandro Sorella. We tackle a careful study of the magnetic phase transition with a combination of static and dynamical mean-field theories, allowing for an easy comparison of competing orders and discrimination of different energetic contributions, all while retaining excellent control of the thermodynamic limit. Remarkably, the accuracy of our DMFT/ED (exact diagonalization based dynamical mean-field theory) estimated critical interaction values and groundstate energies can rival with state-of-the-art quantum Montecarlo literature, while the since believed second order nature of the magnetic transition is challenged by strong evidence of a phase separation region, in which magnetic and topological insulating solutions coexist, leading to a first-order topological transition. To explore the connection to the existing literature we simulate honeycomb nanoflakes, retaining the full point symmetry of the infinte lattice but at finite size, by employing inhomegenous dynamical mean-field theory, which amounts to treating exactly the strong local correlations and modeling at the Hartree-Fock level the weaker spatial correlations in the flake.

Geometry of the electronic ground-state and its relationship to measurable quantities.

• Published: solution to a long-standing paradox about how to properly evaluate the many-electron inverse adiabatic inertia —aka the Drude weight— within bounded crystalline systems. [Phys. Rev. B 102, 205123] (arXiv preprint) {open code for reproducibility}
  
  > The state-of-the-art theory of adiabatic transport, founded by Kohn in the 60s, predicts a vanishing Drude weight at any finite size within open boundary conditions, reflecting the obvious rule out of steady dc currents in a bounded system. Nevertheless at the thermodynamic limit the boundary condition choice must become irrelevant and so the finite value of the Drude weight in a metal has to be recovered also in the OBC case. Inspecting the details of this nontrivial limit has lead to a new effective definition of the OBC Drude-like current response, allowing for highly accurate estimations of the Drude weight even at finite size. 
   
• Long term goal: a local formulation of the Drude weight and its possible relationship with the modern local theory of orbital magnetization.