Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
arXiv:1706.01436 · doi:10.1103/PhysRevB.96.245105
Abstract
We study the emergence of two-dimensional conformal symmetry in critical quantum spin chains on the finite circle. Our goal is to characterize the conformal field theory (CFT) describing the universality class of the corresponding quantum phase transition. As a means to this end, we propose and demonstrate automated procedures which, using only the lattice Hamiltonian as an input, systematically identify the low-energy eigenstates corresponding to Virasoro primary and quasiprimary operators, and assign the remaining low-energy eigenstates to conformal towers. The energies and momenta of the primary operator states are needed to determine the primary operator scaling dimensions and conformal spins -- an essential part of the conformal data that specifies the CFT. Our techniques use the action, on the low-energy eigenstates of , of the Fourier modes of the Hamiltonian density . The were introduced as lattice representations of the Virasoro generators by Koo and Saleur [Nucl. Phys. B 426, 459 (1994)]. In this paper we demonstrate that these operators can be used to extract conformal data in a nonintegrable quantum spin chain.
12 pages, 13 figures, 2 appendices. Title has changed. Many improvements, mainly to the introduction. For a talk see http://pirsa.org/17040033/
References in corpus (8)
- Interacting anyons in topological quantum liquids: The golden chain
- Associative-algebraic approach to logarithmic conformal field theories
- Enlarged symmetry algebras of spin chains, loop models, and S-matrices
- Parafermionic conformal field theory on the lattice
- On critical phases in anisotropic spin-1 chains
- DMRG studies of critical SU(N) spin chains
- Suppression of finite-size effects in one-dimensional correlated systems
- Chiral SU(2)_k currents as local operators in vertex models and spin chains