Quantum criticality in spin chains with non-Ohmic dissipation

Article

关键词: LONG-RANGE INTERACTIONS;    UNIVERSALITY CLASS;    CRITICAL EXPONENTS;    PHASE-TRANSITIONS;    MODEL;    SYSTEMS;   

DOI  :  10.1103/PhysRevB.85.214302

来源: SCIE

【 摘 要 】

We investigate the critical behavior of a spin chain coupled to bosonic baths characterized by a spectral density proportional to omega(s), with s > 1. Varying s changes the effective dimension d(eff) = 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 eta are independent of the order parameter symmetry for all values of s. The dynamical critical exponent varies continuously from z approximate to 2 for s = 1 to z = 1 for s = 2, and the anomalous scaling dimension evolves correspondingly from eta greater than or similar to 0 to eta = 1/4. The latter exponent values are readily understood from the effective dimensionality of the system, being d(eff) approximate to 3 for s = 1, while for s = 2 the anomalous dimension takes the well-known exact value for the two-dimensional Ising and XY models, since then d(eff) = 2. However, a noteworthy feature is that z approaches unity and eta 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,eta = 1/4 for s approximate to 1.75 for both Ising-like and U(1) order parameter symmetry. These results lead us to conjecture that for all site-dissipative Z(q) chains, these two exponents are related by the scaling relation z = max{(2 - eta)/s,1}. We also connect our results to quantum criticality in nondissipative spin chains with long-range spatial interactions.

【 授权许可】

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