High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain

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.

36 pages, 2 figures; v2: references added and updated, more details added on the high-temperature expansion of the jump matrix in section 6, some material moved from appendix C to section 9, figure 2 improved, version to appear in J. Math. Phys

References in corpus (2)

• Equilibrium dynamics of the XX chain
• Dynamical correlation functions of the XXZ model at finite temperature

Cited by in corpus (15)

• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Current operators in integrable models: A review
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Effective free-fermionic form factors and the XY spin chain
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• Chiral basis for qubits and spin-helix decay
• Canonical formulation for the thermodynamics of $s{l}_n$-invariant integrable spin chains