Gabriele Bellomia

Position

PhD

Email

gbellomi@sissa.it

Office

310

Supervisor

Year of Ph.D.

4

## Research interests

**Dynamical mean-field description of strongly correlated 2d materials.**

- Nontrivial competition between in- and out-of-plane magnetic order in the Kane-Mele-Hubbard model. (github project)

> While the well-known Hubbard model on the honeycomb lattice has full SU(2) spin symmetry, thus featuring an isotropic semimetal-to-antiferromagnet transition, the topological spin-orbit coupling introduced by Kane and Mele in 2005 brings in nontrivial frustration effects, resolved —in the thermodynamic limit— into an effective suppression of the out-of-plane AFM order. While this picture has been confirmed by most suitable numerical methods, the relative small size scaling is still debated, with many —yet doubtful— hints at an intermediate quantum spin liquid phase and a strong belief that very small nanoflakes should instead favour out-of-plane magnetization. We tackle the issue with a combination of hartree-fock and (inhomogeneous) dynamical mean-field theory, allowing for an easy comparison of competing orders and discrimination of different energetic contributions.

Remarkably, at the thermodynamic limit, 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.

- New insights on the Mott transition in the 2d Hubbard model, from zero-temperature quasilocal density matrices (github project)

> 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 hints of true*long range*topological order [2], reconnecting to the rich literature proposing the doublon-holon binding as the underlying localization mechanism. Here we embrace a somewhat intermediate approach, moving from some recent works characterizing the Mott transition through a local entropy at finite temperature [3,4] and proposing a criterion to define suitable short ranged reduced density matrices to capture elusive order parameters [5]. Such quasilocal density matrices can be easily retrieved within a CDMFT/ED (*exact diagonalization based cluster dynamical mean-field theory*) framework, by defining a convenient sector-to-Fock-space map for the quantum cluster problem, hence allowing for an efficient bath-tracing algorithm. Such a treatment would allow for a true zero-temperature investigation, refining the stage for an entanglement characterization of the Mott transition.

The quasilocal density matrix could furthermore give easy access to complex real space characterizations, such as the recently proposed*localization marker*[6], which exploits the outstanding local properties of the single-particle density matrix (SPDM) to give a real space probe of electronic localization. Obtaining the full ground-state SPDM in interacting systems is a computationally grievous task, so that capturing the essential physics by means of a quasilocal projection, retrieved at the cost of inhomogeneous CDMFT, would provide a lightweight recipe for strongly correlated materials.

**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.

*Currently working on:*a local formulation of the Drude weight and its possible relationship with the modern local theory of orbital magnetization.