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We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators ⟨σxiσxi+n⟩g,⟨σyiσyi+n⟩g, and ⟨∏ni=1σzi⟩g, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.
|Number of pages||6|
|Journal||Physical Review E: Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 4 Sep 2015|
Bibliographical noteDate of Acceptance: 18/08/2015
1/05/14 → 31/10/17