Institut für Theorie der Kondensierten Materie (TKM)
Soluble limit and criticality of fermions in Z2 gauge theories

TKM Institutsseminar


Elio König


17.12.2020 14:00



MPI for Solid State Research, Stuttgart


Prof. Dr. Mirlin


Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-Tc systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, here we introduce a simple model for fermions moving in the deconfined phase of a Z2 gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. By changing the sign of the plaquette term in the toric code, we are able to tune the groundstate between an orthogonal metal and an orthogonal semimetal, in which the single particle correlators of the original Fermi operators are gapped, despite the existence of gapless collective modes. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. We are able to access the physics beyond the integrable point using a novel diagrammatic perturbation expansion, which allows us to examine various instabilities of the deconfined phase and to derive the Ising (XY) critical theory at the transition between deconfined and confined metal (semimetal). Finally, the connection to quantum information science allows to discuss an analogue quantum emulator (an array of Majorana Cooper pair boxes) for fermions in Z2 gauge theories. Analytical results for this minimal model pave the way for a better understanding of quantum materials with itinerant fermions and the connection to the toric code opens the potential for simulation using upcoming quantum information techniques.

Zoom link: