Double Scaling and Finite Size Corrections in sl(2) 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->\infty for low energies E\sim 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.

arXiv comment23 pages

References in corpus (31)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• How Algebraic Bethe Ansatz works for integrable model
• Classical/quantum integrability in AdS/CFT
• High energy QCD as a completely integrable model
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Stringing Spins and Spinning Strings
• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Yang-Mills Duals for Semiclassical Strings
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Classical/quantum integrability in non-compact sector of AdS/CFT
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• The Algebraic Curve of 1-loop Planar N=4 SYM
• On one-loop correction to energy of spinning strings in S^5
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• On the Large N Limit of the Itzykson-Zuber Integral
• Quasiclassical QCD Pomeron
• Stringy sums and corrections to the quantum string Bethe ansatz
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Quasi-classical Study of Form Factors in Finite Volume
• Wilson loop for large N Yang-Mills theory on a two-dimensional sphere
• 1/J^2 corrections to BMN energies from the quantum long range Landau-Lifshitz model
• Fluctuations and Energy Shifts in the Bethe Ansatz
• Multiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture
• WKB quantization of reggeon compound states in high-energy QCD

Cited by in corpus (31)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• Universal cumulants of the current in diffusive systems on a ring
• Logarithmic scaling in gauge/string correspondence
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Green-Schwarz Strings in TsT-transformed backgrounds
• Integrability and Transcendentality
• Complete 1-loop test of AdS/CFT
• Tailoring Three-Point Functions and Integrability III. Classical Tunneling
• How Accurate is the Quantum String Bethe Ansatz?
• Y-system and Quasi-Classical Strings
• Constructing the AdS/CFT dressing factor
• Strings as Multi-Particle States of Quantum Sigma-Models
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Quantum integrability and functional equations
• Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution
• Universality in dynamical phase transitions of diffusive systems
• Quantum corrections to energy of short spinning string in AdS5
• On the finite size corrections of anti-ferromagnetic anomalous dimensions in $\mathcal{N}=4$ SYM
• Quantum Stability for the Heisenberg Ferromagnet
• Hubbard's Adventures in $\mathcal{N}=4$ SYM-land? Some non-perturbative considerations on finite length operators
• Lectures on the integrability of the 6-vertex model
• Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
• Strong coupling expansion of Baxter equation in N=4 SYM
• "Short" spinning strings and structure of quantum AdS_5 x S^5 spectrum
• Finite-size corrections to the rotating string and the winding state
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• Open giant magnons on LLM geometries
• On the Construction of Correlation Functions for the Integrable Supersymmetric Fermion Models
• KPZ fluctuations in finite volume
• On the short string limit of the folded spinning string in AdS5 x S5