Quantum spin chains and riemann zeta function with odd arguments

H. E. Boos; E. Korepin V

doi:10.1088/0305-4470/34/26/301

Quantum spin chains and riemann zeta function with odd arguments

H. E. Boos
, E. Korepin V

Institute for Theoretical Physics

Institute for High Energy Physics

Research output: Contribution to journal › Article › peer-review

87 Scopus citations

Abstract

The Riemann zeta function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann zeta function with odd arguments.

Original language	English
Pages (from-to)	5311-5316
Number of pages	6
Journal	Journal of Physics A: Mathematical and General
Volume	34
Issue number	26
DOIs	https://doi.org/10.1088/0305-4470/34/26/301
State	Published - Jul 6 2001

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title = "Quantum spin chains and riemann zeta function with odd arguments",

abstract = "The Riemann zeta function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann zeta function with odd arguments.",

author = "Boos, \{H. E.\} and \{Korepin V\}, E.",

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T1 - Quantum spin chains and riemann zeta function with odd arguments

AU - Boos, H. E.

AU - Korepin V, E.

PY - 2001/7/6

Y1 - 2001/7/6

N2 - The Riemann zeta function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann zeta function with odd arguments.

AB - The Riemann zeta function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann zeta function with odd arguments.

UR - https://www.scopus.com/pages/publications/0035816523

U2 - 10.1088/0305-4470/34/26/301

DO - 10.1088/0305-4470/34/26/301

M3 - Article

AN - SCOPUS:0035816523

SN - 0305-4470

VL - 34

SP - 5311

EP - 5316

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 26

ER -

Quantum spin chains and riemann zeta function with odd arguments

Abstract

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