Transition asymptotics of Toeplitz determinants and emergence of Fisher–Hartwig representations

DOI10.1088/1361-6544/ab127azbMath1428.82014OpenAlexW2943569253MaRDI QIDQ5230490

Kasia Kozlowska, Jani A. Virtanen

Publication date: 23 August 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/ab127a

zbMATH Keywords

quantum spin chainsToeplitz determinantsXY modelFisher-Hartwig singularitiestransition asymptoticsdouble-scaling limits

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27) Riemann-Hilbert problems in context of PDEs (35Q15) Statistical mechanics of magnetic materials (82D40) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (2)

Uniform asymptotics of Toeplitz determinants with Fisher-Hartwig singularities ⋮ Entanglement entropies of an interval in the free Schrödinger field theory at finite density

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An introduction to integrable techniques for one-dimensional quantum systems
• Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
• Emergence of a singularity for Toeplitz determinants and Painlevé V
• Monodromy problem and the boundary condition for some Painlevé equations
• Random matrix theory and entanglement in quantum spin chains
• Toeplitz determinants with merging singularities
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Quantum spin chain, Toeplitz determinants and the Fisher-Hartwig conjecture
• Two soluble models of an antiferromagnetic chain
• On the asymptotics of a Toeplitz determinant with singularities
• A Lattice Model of Liquid Helium, I
• Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump
• Emptiness Formation Probability for the One-Dimensional IsotropicXYModel
• Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results
• Asymptotics of Toeplitz determinants and the emptiness formation probability for the XY spin chain

This page was built for publication: Transition asymptotics of Toeplitz determinants and emergence of Fisher–Hartwig representations