2007/04/30 by J. A. Hoyos, José A. Hoyos, André P. Vieira +2 · 2 citations
Mathematics · Physics and Astronomy · #Amplitude #Antiferromagnetism #Correlation function (quantum field theory) #Entropy (arrow of time) #Exponent #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Spin (aerodynamics) #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.76.174425
published as Phys. Rev. B 76, 174425 (2007) · v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and statistics, references added, published version
arxiv created 2007/11/15 · openalex publication_date 2007/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1∕2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=\ensuremathυl^\ensuremath-\ensuremathη. In addition to the well-known universal (disorder-independent) power-law exponent \ensuremathη=2, we find interesting universal features displayed by the prefactor \ensuremathυ=\ensuremathυo∕3, if l is odd, and \ensuremathυ=\ensuremathυe∕3, otherwise. Although \ensuremathυo and \ensuremathυe are nonuniversal (disorder dependent) and distinct in magnitude, the combination \ensuremathυo+\ensuremathυe=\ensuremath-1∕4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.