Double scaling and finite size corrections in spin chain

Abstract

We find explicit expressions for two first finite size corrections to the distribution of Bethe roots, the asymptotics of energy and high conserved charges in the sl(2) quantum Heisenberg spin chain of length J in the thermodynamical limit J → ∞ for low lying states with energies E ∼ 1/J. This limit was recently studied in the context of integrability in perturbative N = 4 super-Yang-Mills theory. We applied the double scaling technique to Baxter equation, similarly to the one used for large random matrices near the edge of the eigenvalue distribution. The positions of Bethe roots are described near the edge by zeros of Airy function. Our method can be generalized to any order in 1/J. It should also work for other quantum integrable models.

Universal cumulants of the current in diffusive systems on a ring

“…These finite size corrections are similar to the ones calculated recently for spin chains in the context of quantum strings [29,30].…”

“…These finite corrections have been calculated recently, starting from the Bethe ansatz equations, for several spin chains in the context of string theory and expressions very similar to our F have been obtained [29]. Note also that a more systematic approach has been developed to calculate the next finite size correction [30].…”

“…near the singularities of g(k). A more detailed analysis of these two neighborhoods would only contribute to higher orders in the 1/L expansion [30].…”

Foundations of the AdS5× S5superstring: I

“…More precisely, as can be seen from (2.115) and (2.123), a dynamical supersymmetry generator has the following generic structure 129) where the parameter α in the exponent of (2.129) is equal to α = 1/2(ǫ A − ǫ B ), and, therefore, α = 1/2 for supercharges Q andQ, and α = −1/2 for supercharges Q † and Q † . Then, the function Ω(x, p, χ; g) is a local function of transversal bosonic fields and fermionic variables.…”

Generalized scaling function at strong coupling

“…At two loops the discreet behavior of the Bethe roots u k becomes important [25]. In this paper we will show how to efficiently override these difficulties and rewrite (1.1) as a quadratic equation.…”