Emergent Geometry in Quantum Matter

by Giandomenico Palumbo (CFisUC)

Wednesday 29 Apr 2026, 14:00 → 15:00 Portugal

Sala de Conferências (Departamento de Física FCTUC)

Geometry plays a central role in modern physics. For instance, in general relativity, geometry is not a background structure but the dynamical manifestation of gravity itself. In condensed matter systems, however, geometry can appear in a different and more unexpected way: it can emerge as a collective property of quantum many-body states, without being a fundamental input of the theory.
In this talk, I will discuss concrete realisations of emergent geometry in quantum matter. I will first focus on the fractional quantum Hall effect, where strong interactions give rise to an intrinsic geometric degree of freedom. This structure is naturally connected to non-commutative geometry and supports collective excitations with the character of a spin-2 “graviton”-like mode.
I will then turn to band theory, where geometry arises already at the single-particle level. The quantum geometric tensor endows the space of quantum states with a notion of distance, known as quantum metric, revealing a hidden geometric structure in Bloch bands that has direct physical consequences. A central theme of my talk will be the distinction between geometry as a fundamental or externally imposed structure (as in gravity or lattice deformations in quantum materials) and geometry as an emergent feature of quantum states.