Bose-Einstein condensation in diamond hierarchical lattices

Area of Science:

• Condensed Matter Physics
• Quantum Statistics
• Statistical Mechanics

Background:

• Bose-Einstein condensation (BEC) is a quantum phenomenon observed in bosons at low temperatures.
• Hierarchical lattices present unique structures that can influence quantum phenomena.
• Understanding BEC on complex geometries is crucial for exploring novel quantum states.

Purpose of the Study:

• Investigate Bose-Einstein condensation of noninteracting particles on hierarchical diamond lattices.
• Analyze the impact of lattice structure, defined by branching parameter q and generation number n, on BEC.
• Characterize the critical behavior and transition temperature of the BEC phase.

Main Methods:

• Utilized a tight-binding single-particle Hamiltonian with rescaled hopping amplitudes.
• Employed an orthogonal basis transformation to map the system onto decoupled linear chains.
• Performed finite-size scaling analysis of condensed particle fraction and specific heat.

Main Results:

• The integrated density of states reveals a fractal structure with power-law decay.
• The spectral dimension matches the topological dimension of the lattice.
• Critical exponents for the BEC transition follow power-law spectral density behavior, showing non-mean-field values for d(s) < 4.
• Transition temperature increases with the branching parameter q.

Conclusions:

• Bose-Einstein condensation on hierarchical diamond lattices exhibits fractal characteristics.
• The critical behavior is governed by the lattice's spectral dimension, deviating from mean-field theory in certain regimes.
• The transition temperature shows a clear dependence on the lattice's branching parameter.