Speaker: Jan Schneider
Affiliation: IFF
Date: Tuesday, 3 February 2026 at 12:00
Location: Seminar Room, Serrano 121 (CFMAC)
As we have have a couple of new members, especially younger ones, I wanted to take the time and briefly introduce Tensor Networks as a state-of-the-art numerical method and advertise its benefits and use. I will briefly introduce Matrix Product States (MPS) and the DMRG algorithm.
Then I will discuss the findings of https://doi.org/10.21468/SciPostPhys.18.4.142; the puzzling features of the MPS transfer matrix spectrum at a critical point. We set up an effective field theory formulation for the renormalization flow of MPS with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension χ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing χ, the infrared scale, set by the correlation length ξ(χ), increases, while the strength of the perturbation at the lattice scale decreases