Dissipation-induced bulk and boundary criticality in the Haldane chain

Abstract

We study the Haldane chain coupled to a dissipative ohmic bath. Using large-scale quantum Monte Carlo simulations, we identify a second-order quantum phase transition into an antiferromagnetic state with spontaneously broken SO(3) symmetry that is governed by an interacting fixed point with dynamical exponent $z\approx 2$. We derive a generalized string order parameter which indicates that the symmetry-protected topological ground state of the Haldane chain is stable for weak dissipation and develops a nontrivial scaling dimension at criticality. In particular, its topological edge modes display nontrivial boundary criticality that is distinct from an equivalent transition out of a trivial state; for the latter, we perform an accurate $\epsilon$ expansion of a dissipative ${\varphi }^4$ theory with ordinary boundary conditions. Our setup realizes a spin impurity in a critical yet nonconformal antiferromagnet and paves the way for continuously tunable boundary criticality controlled by dissipation.