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Dissipation-Induced Order: The $S=1/2$ Quantum Spin Chain Coupled to an Ohmic Bath

We consider an $S=1/2$ antiferromagnetic quantum Heisenberg chain where each site is coupled to an independent bosonic bath with ohmic dissipation. The coupling to the bath preserves the global SO(3) spin symmetry. Using large-scale, approximation-free quantum Monte Carlo simulations, we show that any finite coupling to the bath suffices to stabilize long-range antiferromagnetic order. This is in stark contrast to the isolated Heisenberg chain where spontaneous breaking of the SO(3) symmetry is forbidden by the Mermin-Wagner theorem. A linear spin-wave theory analysis confirms that the memory of the bath and the concomitant retarded interaction stabilize the order. For the Heisenberg chain, the ohmic bath is a marginal perturbation so that exponentially large system sizes are required to observe long-range order at small couplings. Below this length scale, our numerics is dominated by a crossover regime where spin correlations show different power-law behaviors in space and time. We discuss the experimental relevance of this crossover phenomena.