Quantum coherence at the quantum phase transition in a random Heisenberg spin system with Dzyaloshinskii–Moriya interaction

The quantum coherence between non-nearest spin blocks in a one-dimensional random Heisenberg spin chain with Dzyaloshinskii–Moriya (DM) interaction at absolute zero temperature has been investigated. Using the quantum renormalization group method, we study the variation of quantum coherence with random coupling parameters and DM interaction especially when the size of the system becomes larger. The random coupling parameter follows the normal distribution, and its standard deviation reflects the disorder degree of the system. When the standard deviation is zero, the system is ordered. At the quantum critical point, the quantum coherence has a significant discontinuous change from zero to maximum. As the standard deviation becomes nonzero, the “smoothing” of the coherence near the quantum phase transition point is observed. When the standard deviation is large, the minimum value of the average quantum coherence is no longer zero, and there exists always quantum coherence in the random system. The larger the standard deviation, the larger the fluctuation range of quantum coherence. The fluctuation distribution of quantum coherence is becoming more and more asymmetric around the quantum phase transition point. When the average coherence is small, the fluctuation of coherence is larger, indicating that the effect of disorder is more obvious. Our results also show that the position of the maximum quantum coherence fluctuation can be used to indicate the critical point of quantum phase transition of the system.