title: Random matrix theory and critical phenomena in quantum spin chains.
abstract: 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 〈σ_{i}^{x}σ_{i+n}^{x}〉_{g},〈σ_{i}^{y}σ_{i+n}^{y}〉_{g}, and 〈∏_{i=1}^{n}σ_{i}^{z}〉_{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.
authors.affiliation: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors.forename: J
authors.initials: J
authors.lastname: Hutchinson
authors.affiliation: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors.forename: J P
authors.initials: JP
authors.lastname: Keating
authors.affiliation: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors.forename: F
authors.initials: F
authors.lastname: Mezzadri