Quantum spin chains with bond dissipation

Abstract

We study the effect of bond dissipation on the one-dimensional antiferromagnetic spin-$1/2$ Heisenberg model. In analogy to the spin-Peierls problem, the dissipative bath is described by local harmonic oscillators that modulate the spin exchange coupling, but instead of a single boson frequency we consider a continuous bath spectrum $\propto \omega^s$. Using an exact quantum Monte Carlo method for retarded interactions, we show that for $s<1$ any finite coupling to the bath induces valence-bond-solid order, whereas for $s>1$ the critical phase of the isolated chain remains stable up to a finite critical coupling. We find that, even in the presence of the gapless bosonic spectrum, the spin-triplet gap remains well defined for any system size, from which we extract a dynamical critical exponent of $z=1$. We provide evidence for a Berezinskii-Kosterlitz-Thouless quantum phase transition that is governed by the SU(2)$_1$ Wess-Zumino-Witten model. Our results suggest that the critical properties of the dissipative system are the same as for the spin-Peierls model, irrespective of the different interaction range, i.e., power-law vs. exponential decay, of the retarded dimer-dimer interaction, indicating that the spin-Peierls criticality is robust with respect to the bosonic density of states.