Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime (Q2826720)

The authors derive efficient series representations for the two-point correlation functions of the Hamiltonian NEWLINE\[NEWLINEH=J\sum\limits_{j=-L+1}^{L}{\left( \sigma _{j-1}^{x}\sigma _{j}^{x}+\sigma _{j-1}^{y}\sigma _{j}^{y}+ \Delta (\sigma _{j-1}^{z}\sigma _{j}^{z}-1) \right)}-\frac{h}{2}\sum\limits_{j=-L+1}^{L}{\sigma _{j}^{z}}, NEWLINE\]NEWLINE where \(J > 0\) is a coupling constant measuring the strength of the exchange interaction, \(\Delta\) is the longitudinal anisotropy in the couplings, \(h\) is an external magnetic field and the \(\sigma _{j}^{\alpha}\) are Pauli matrices. The authors consider the spectrum of correlation lengths of the spin-\(\frac{1}{2}\) \(XXZ\) chain in the antiferromagnetic massive regime for the spectrum and Bethe root patterns of the quantum transfer matrix in the antiferromagnetic massive regime at finite magnetic field \(h\). The results are based on [the authors, J. Phys. A, Math. Theor. 48, No. 33, Article ID 334001, 38 p. (2015; Zbl 1329.82023)]. Then, the authors present new results for the amplitudes in the form factor series in the low-temperature limit. They show how the form factor series can be written as series of multiple integrals corresponding to integration over particle and hole parameters. The authors compare their results with previous results which were interpreted in terms of multi-spinon contributions and they perform numerical tests against known exact results and purely numerical calculations in order to assess the efficiency of the novel series representations. The isotropic limit is discussed. In order to describe the low-temperature spectrum of correlation length the authors introduce a number of functions that determine the physical properties of the \(XXZ\) chain at \(T = 0^+\). The authors obtain rather explicit expressions for form factor densities in the limit which are different from those obtained for the usual transfer matrix given in [the authors, ``On form-factor expansions for the \(XXZ\) chain in the massive regime'', J. Stat. Mech. Theory Exp. 2015, No. 5, Article ID P05037, 49 p. (2015; \url{doi:10.1088/1742-5468/2015/05/P05037})]. They derive novel form factor series representations for the ground state two-point correlation function of the \(XXZ\) chain in the antiferromagnetic massive regime and of the \(XXX\) chain at vanishing magnetic field. The authors show that the spectrum of correlation lengths of the quantum transfer matrix can be entirely classified in terms of particle-hole excitations. The explicit form of the function \(\rho^{(0)}_n\) for \(-\gamma< \mathrm{Im} x < 0\) is calculated. Lastly, the authors give almost all technical details of the calculations in a series of appendices.