We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.
Cited by 8
Etienne Granet, Low-density limit of dynamical correlations in the Lieb–Liniger model
J. Phys. A: Math. Theor. 54, 154001 (2021) [Crossref]
Isabelle Bouchoule et al., The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
SciPost Phys. 9, 044 (2020) [Crossref]
Constantin Babenko et al., A thermal form factor series for the longitudinal two-point function of the Heisenberg–Ising chain in the antiferromagnetic massive regime
Journal of Mathematical Physics 62, 041901 (2021) [Crossref]
K. L. Zhang et al., Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures
Phys. Rev. Lett. 126, 116401 (2021) [Crossref]
Etienne Granet et al., A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
SciPost Phys. 9, 082 (2020) [Crossref]
Miłosz Panfil, The two particle–hole pairs contribution to the dynamic correlation functions of quantum integrable models
J. Stat. Mech. 2021, 013108 (2021) [Crossref]
Oleksandr Gamayun et al., Effective free-fermionic form factors and the XY spin chain
SciPost Phys. 10, 070 (2021) [Crossref]
Pasquale Calabrese, Entanglement spreading in non-equilibrium integrable systems
SciPost Phys. Lect. Notes, 20 (2020) [Crossref]
Ontology / TopicsSee full Ontology or Topics database.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Rudolf Peierls Centre for Theoretical Physics, University of Oxford
- 2 Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]