2012/04/30 by Iver Bakken Sperstad, Einar B. Stiansen, Asle Sudbø · 1 citation
Physics and Astronomy · #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.85.214302
published as Physical Review B 85, 214302 (2012) · 8 pages, 6 figures
arxiv created 2012/06/12 · arxiv updated 2012/06/13
We investigate the critical behavior of a spin chain coupled to bosonic baths characterized by a spectral density proportional to ωs, with s>1. Varying s changes the effective dimension deff = d + z of the system, where z is the dynamical critical exponent and the number of spatial dimensions d is set to one. We consider two extreme cases of clock models, namely Ising-like and U(1)-symmetric ones, and find the critical exponents using Monte Carlo methods. The dynamical critical exponent and the anomalous scaling dimension η are independent of the order parameter symmetry for all values of s. The dynamical critical exponent varies continuously from z ≈ 2 for s=1 to z=1 for s=2, and the anomalous scaling dimension evolves correspondingly from η\gtrsim 0 to η= 1/4. The latter exponent values are readily understood from the effective dimensionality of the system being deff ≈ 3 for s=1, while for s=2 the anomalous dimension takes the well-known exact value for the 2D Ising and XY models, since then d_\rmeff=2. A noteworthy feature is, however, that z approaches unity and η approaches 1/4 for values of s < 2, while naive scaling would predict the dissipation to become irrelevant for s=2. Instead, we find that z=1,η=1/4 for s ≈ 1.75 for both Ising-like and U(1) order parameter symmetry. These results lead us to conjecture that for all site-dissipative Zq chains, these two exponents are related by the scaling relation z = max (2-η)/s, 1. We also connect our results to quantum criticality in nondissipative spin chains with long-range spatial interactions.