2019/11/30 by Minjae Jo, B. Kahng · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.101.022121
published as Phys. Rev. E 101, 022121 (2020) · 16 pages, 21 figures
arxiv created 2020/01/31 · arxiv updated 2020/02/21
Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semi-classical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited s state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the d state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of ∼ 1/rd+σ (denoted as LTDP), where r is the separation, d is the spatial dimension, and σ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension dc= min(3, 1.5σ). We numerically obtain a set of critical exponents in the LTDP class and determine the interval of σ for the LTDP class. Finally, we construct a diagram of universality classes in the space (d, σ).