A. Szabo: Accurate conformal data from entanglement in rainbow chains

Obtaining details of the underlying 2D conformal field theory (CFT) from wave functions is a challenge both for edges of chiral topological orders and for critical spin chains. In this talk, I will discuss a method to overcome the latter challenge [1]. By mapping CFT reduced density matrices to thermal ones, I show that the ground-state entanglement spectra of chains with exponentially decaying terms recover conformal towers of the associated boundary CFT, which have the same structure as chiral conformal towers. Crucially, the logarithmic finite-size scaling of entanglement spectra in uniform chains [2] is replaced by power laws for these "rainbow chains" [3], thus yielding sharp conformal multiplets for much smaller system sizes. Through free-fermion and interacting examples, I will demonstrate that such chains are an efficient tool to obtain detailed CFT spectra from single wave functions without access to the parent Hamiltonian. This makes them promising for studying the edge physics of, e.g., chiral spin liquids, which are routinely described in terms of projected parton wave functions. I will also discuss an MPS-based Wilsonian numerical renormalisation group (NRG) scheme for solving interacting rainbow chains, which can handle chains with Hamiltonian terms spanning several orders of magnitude without numerical instabilities. I will show that the fixed-point tensor of this NRG also encodes scaling dimensions of the full CFT, thus making it a promising tool for extracting additional CFT data, such as fusion and OPE coefficients and modular matrices. [1] A. Szabó. Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra. https://arxiv.org/abs/2412.09685 [2] A. Läuchli. Operator content of real-space entanglement spectra at conformal critical points. https://arxiv.org/abs/1303.0741 [3] G. Vitagliano, A. Riera and J. I. Latorre. Volume-law scaling for the entanglement entropy in spin-1/2 chains. https://doi.org/10.1088/1367-2630/12/11/113049