Conformal Field Theories as Scaling Limit of Anyonic Chains

Abstract

We provide a mathematical definition of a low energy scaling limit of a sequence of general non-relativistic quantum theories in any dimension, and apply our formalism to anyonic chains. We formulate Conjecture 4.3 on conditions when a chiral unitary rational (1+1)-conformal field theory would arise as such a limit and verify the conjecture for the Ising minimal model $M(4,3)$ using Ising anyonic chains. Part of the conjecture is a precise relation between Temperley-Lieb generators $\{e_i\}$ and some finite stage operators of the Virasoro generators $\{L_m+L_{-m}\}$ and $\{i(L_m-L_{-m})\}$ for unitary minimal models $M(k+2,k+1)$ in Conjecture 5.5. A similar earlier relation is known as the Koo-Saleur formula in the physics literature [39]. Assuming Conjecture 4.3, most of our main results for the Ising minimal model $M(4,3)$ hold for unitary minimal models $M(k+2,k+1),k\ge 3$ as well. Our approach is inspired by an eventual application to an efficient simulation of conformal field theories by quantum computers, and supported by extensive numerical simulation and physical proofs in the physics literature.

To appear in CMP

References in corpus (5)

• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Parafermionic conformal field theory on the lattice
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Categorification and correlation functions in conformal field theory
• Scale invariant transfer matrices and Hamiltionians

Cited by in corpus (1)

• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states