Tricritical directed percolation with long-range interaction in one and two dimensions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Systems

Background:

• The quantum contact process involves coherent and incoherent branching and coagulation in driven open quantum spin systems.
• A semiclassical approach reveals quantum coherence effects involving atomic excitation and transitions, leading to a tricritical point belonging to the tricritical directed percolation (TDP) class.

Purpose of the Study:

• To extend the TDP model to incorporate long-range interactions induced by atomic excitation to the d-state.
• To investigate the properties of this new long-range interacting TDP (LTDP) universality class.
• To construct a universality class diagram in the (d,σ) space.

Main Methods:

• Theoretical extension of the TDP model to include long-range interactions of the form ~1/r^(d+σ).
• Numerical investigation of the LTDP class below the upper critical dimension d_c = min(3, 1.5σ).
• Determination of critical exponents and the parameter interval for the LTDP class.

Main Results:

• A new LTDP universality class with long-range interactions was defined.
• Critical exponents for the LTDP class were numerically obtained.
• The interval of the control parameter σ for the LTDP class was determined.

Conclusions:

• The study successfully extends the TDP model to account for long-range interactions in quantum spin systems.
• A comprehensive diagram of universality classes in the (d,σ) space was constructed.
• The findings provide insights into the critical behavior of quantum systems with competing interactions.