Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain - F. Azad; Adam J. McRoberts; Chris Hooley; A. G. Green (Physical Review Research)
We study the J_{1}-J_{2} spin-1/2 chain using a path integral constructed over matrix product states (MPS). By virtue of its nontrivial entanglement structure, the MPS ansatz captures the key phases of the model even at a semiclassical, saddle-point level, and, as a variational state, is in good agreement with the field theory obtained by Abelian bosonization. Going beyond the semiclassical level, we show that the MPS ansatz facilitates a physically motivated derivation of the field theory of the critical phase: By carefully taking the continuum limit—a generalization of the Haldane map—we recover from the MPS path integral a field theory with the correct topological term and emergent SO(4) symmetry, constructively linking the microscopic states and topological field-theoretic structures. Moreover, the dimerization transition is particularly clear in the MPS formulation—an explicit dimerization potential becomes relevant, gapping out the magnetic fluctuations.