Entanglement and quantum phase transition of spin glass: A renormalization group approach

• Concurrence for two spin glass models are obtained by Kadanoff renormalization group approach.
• For Δ=0Δ=0, a first-order phase transition is expected.
• By varying Δ from 0.05 to 0.5, the spin glass effect broadens the sharp transition.
• The spin glass effect causes a change in first-order to second-order transition.
• Fluctuations in the average concurrence for spin glass is a good indicator of quantum phase transition.

Using a renormalization group approach, we study the entanglement properties of two spin glass models: the XXZ   Heisenberg (with Dzyaloshinskii–Moriya interaction) and Ising transverse field spin glasses. The concurrence for both models are obtained through the Kadanoff renormalization group (RG) approach with random Jiz and JiJi respectively. The constant couplings in the RG flow are randomized through the Gaussian distribution. For Δ=0Δ=0 corresponding to a non-spin glass material, a first-order transition is expected. By varying Δ from 0.05 to 0.5, the spin glass effect broadens the sharp transition resulting in a second-order-like transition. The fluctuations in the average concurrence for the spin glass case as measured by the standard deviations is also a good indicator of quantum phase transition.