For the finite-temperature XX chain in the spacelike regime, the paper derives the exact leading asymptotic term of the transverse two-point function, including the previously undetermined amplitude C(T,h).
High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain
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abstract
We analyse the transverse dynamical two-point correlation function of the XX chain by means of a thermal form factor series. The series is rewritten in terms of the resolvent and the Fredholm determinant of an integrable integral operator. This connects it with a matrix Riemann-Hilbert problem. We express the correlation function in terms of the solution of the matrix Riemann-Hilbert problem. The matrix Riemann-Hilbert problem is then solved asymptotically in the high-temperature limit. This allows us to obtain the leading high-temperature contribution to the two-point correlation function at any fixed space-time separation.
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Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime
For the finite-temperature XX chain in the spacelike regime, the paper derives the exact leading asymptotic term of the transverse two-point function, including the previously undetermined amplitude C(T,h).