2018/05/09 by Yan-Wei Dai, Dai, Yan-Wei, Xi-Hao Chen +8
Physics and Astronomy · #FOS: Physical sciences #Opinion Dynamics and Social Influence #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.1805.03464
11 pages; 8 figures
arxiv created 2018/05/09 · openalex publication_date 2018/05/09 · arxiv updated 2018/05/10 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28
We numerically investigate classical and quantum correlations in one-dimensional quantum critical systems. The infinite matrix product state (iMPS) representation is employed in order to consider an infinite-size spin chain. By using the infinite time-evolving block decimation algorithm, iMPS ground state wave functions are obtained at critical points for the transverse-field spin-1/2 XY model. From the ground state wave functions, we calculate classical and quantum correlations and mutual information. All of the correlations are found to exhibit a power-law decay with the increments of the lattice distance for both the transition lines of the Ising universality class and the Gaussian universality class. Such power-law scaling behaviors of the correlations manifest the existence of diversing correlation lengths, which means scale invariance. The critical features of the correlations can be characterized by introducing a critical exponent of the power-law decaying correlations. Similar to the critical exponent η of the spin-spin correlation for the universality classes in the transverse-field XY model, we calculate the critical exponents of the two-spin classical and quantum correlations as well as that of the corresponding mutual information. All of the correlations have the same critical exponents, i.e., ηI=ηC=ηD at a critical point, where the superscripts I, C, and D stand for mutual information, classical correlation, and quantum correlation, respectively. Furthermore, the critical exponent η of the spin-spin correlation is shown to relate to η= ηα/2 with α∈ \ I, C, D\.