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 $s$, $\nu$ and $z$, corresponding to the energy gap, correlation length and dynamic exponent respectively. We also compute the ground state correlators ${⟨{\sigma }_i^x{\sigma }_{i+n}^x⟩}_g$, ${⟨{\sigma }_i^y{\sigma }_{i+n}^y⟩}_g$ and ${⟨{\prod }_{i=1}^n{\sigma }_i^z⟩}_g$, 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.

14 pages

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Cited by in corpus (6)

• Entanglement in fermionic chains with finite range coupling and broken symmetries
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• Fisher Hartwig determinants, conformal field theory and universality in generalised XX models
• On relations between one-dimensional quantum and two-dimensional classical spin systems