Detecting emergent continuous symmetries at quantum criticality

TL;DR

This paper introduces a tensor network algorithm to identify emergent continuous symmetries and conserved currents in quantum spin chains, enabling analysis without prior low-energy theory knowledge.

Contribution

It presents a novel numerical method to extract lattice operators for emergent symmetries directly from ground states of quantum spin chains.

Findings

Successfully applied to spin-1/2 J-Q Heisenberg chain

Identified lattice Kac-Moody generators at quantum critical points

Can find local integrals of motion and parent Hamiltonians

Abstract

New or enlarged symmetries can emerge at the low-energy spectrum of a Hamiltonian that does not possess the symmetries, if the symmetry breaking terms in the Hamiltonian are irrelevant under the renormalization group flow. In this letter, we propose a tensor network based algorithm to numerically extract lattice operator approximation of the emergent conserved currents from the ground state of any quantum spin chains, without the necessity to have prior knowledge about its low-energy effective field theory. Our results for the spin-1/2 $J$-$Q$ Heisenberg chain and a one-dimensional version of the deconfined quantum critical points (DQCP) demonstrate the power of our method to obtain the emergent lattice Kac-Moody generators. It can also be viewed as a way to find the local integrals of motion of an integrable model and the local parent Hamiltonian of a critical gapless ground state.