TY - JOUR

T1 - Quantum correlations and number theory

AU - Boos, H. E.

AU - Korepin, V. E.

AU - Nishiyama, Y.

AU - Shiroishi, M.

N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2002/5/24

Y1 - 2002/5/24

N2 - We study the spin-1/2 Heisenberg XXX antiferromagnet for which the spectrum of the Hamiltonian was found by Bethe in 1931. We study the probability of the formation of ferromagnetic string in the antiferromagnetic ground state, which we call emptiness formation probability P(n). This is the most fundamental correlation function. We prove that, for short strings, it can be expressed in terms of the Riemann zeta function with odd arguments, logarithm In 2 and rational coefficients. This adds yet another link between statistical mechanics and number theory. We have obtained an analytical formula for P(5) for the first time. We have also calculated P(n) numerically by the density matrix renormalization group. The results agree quite well with the analytical results. Furthermore, we study the asymptotic behaviour of P(n) at finite temperature by quantum Monte Carlo simulation. This also agrees with our previous analytical results.

AB - We study the spin-1/2 Heisenberg XXX antiferromagnet for which the spectrum of the Hamiltonian was found by Bethe in 1931. We study the probability of the formation of ferromagnetic string in the antiferromagnetic ground state, which we call emptiness formation probability P(n). This is the most fundamental correlation function. We prove that, for short strings, it can be expressed in terms of the Riemann zeta function with odd arguments, logarithm In 2 and rational coefficients. This adds yet another link between statistical mechanics and number theory. We have obtained an analytical formula for P(5) for the first time. We have also calculated P(n) numerically by the density matrix renormalization group. The results agree quite well with the analytical results. Furthermore, we study the asymptotic behaviour of P(n) at finite temperature by quantum Monte Carlo simulation. This also agrees with our previous analytical results.

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U2 - 10.1088/0305-4470/35/20/305

DO - 10.1088/0305-4470/35/20/305

M3 - Article

AN - SCOPUS:0037166217

VL - 35

SP - 4443

EP - 4451

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 20

ER -