dorsal/arxiv
View SchemaPainlev\'e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point
| Authors | Fabian H. L. Essler, Holger Frahm, Alexander R. Its, Vladimir E. Korepin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9604005 |
| URL | https://arxiv.org/abs/solv-int/9604005 |
| DOI | 10.1088/0305-4470/29/17/032 |
| Journal | J.Phys.A29:5619-5626,1996 |
Abstract
We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field $h_c$ (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra.
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"abstract": "We consider quantum correlation functions of the antiferromagnetic\nspin-$\\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that\nfor a magnetic field close to the critical field $h_c$ (for the critical\nmagnetic field the ground state is ferromagnetic) certain correlation functions\ncan be expressed in terms of the solution of the Painlev\\\u0027e V transcendent.\nThis establishes a relation between solutions of Painlev\\\u0027e differential\nequations and quantum correlation functions in models of {\\sl interacting}\nfermions. Painlev\\\u0027e transcendents were known to describe correlation functions\nin models with free fermionic spectra.",
"arxiv_id": "solv-int/9604005",
"authors": [
"Fabian H. L. Essler",
"Holger Frahm",
"Alexander R. Its",
"Vladimir E. Korepin"
],
"categories": [
"solv-int",
"cond-mat",
"hep-th",
"nlin.SI"
],
"doi": "10.1088/0305-4470/29/17/032",
"journal_ref": "J.Phys.A29:5619-5626,1996",
"title": "Painlev\\\u0027e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point",
"url": "https://arxiv.org/abs/solv-int/9604005"
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