Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

Abstract

We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator matrix elements and is not model specific.We discuss only models with well defined asymptotic states. For such models the long time, large distance asymptotics of the correlation functions fall into two universality classes. These classes differ primarily by whether the behavior of the two-particle S matrix at low momenta is diagonal or corresponds to pure reflection. We discuss similarities and differences between our results and results obtained by the semi-classical method suggested by Sachdev and Young, Phys. Rev. Lett. 78, 2220Lett. 78, (1997.

Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in anXXZchain

“…42,[65][66][67][68][69][70][71][72][73] For massive 1D systems, Sachdev and Damle 71 gave well-reasoned arguments that transport at T > 0 should be diffusive. This is also the naive expectation for a 1+1-D theory, in the absence of other special properties.…”

“…However, Bethe ansatz results on integrable models appear to support the possibility of a non-zero Drude weight at non-zero temperature, indicative of ballistic transport. 72,73 One might expect that the incorporation of an integrability breaking perturbation (such as an irrelevant operator) introduces an additional time scale, beyond which the space-time retarded Green's function for the appropriate observable (e.g. a spin-spin correlation function) would transition from ballistic to diffusive behavior.…”

Finite-temperature correlation function for the one-dimensional quantum Ising model: The virial expansion

“…For these results to have a greater use one has to establish their relationship with the formfactor approach. A step in this direction was made in [8] where the semiclassical results [5], [6], [7] were reproduced by summing up the leading singularities in the formfactor expansion. Such summation was restricted to the leading order in the soliton density n ∼ exp(−M/T ) (M is the spectral gap).…”

Critical conductance of a one-dimensional doped Mott insulator

“…14 ͑In the exact commensurate case of an undoped Mott insulator the fate of the Drude weight is less clear and remains a subject of ongoing research. 15,16 ͒ Remarkably, the knowledge of the Drude weight in the conductivity of a uniform 1D system is insufficient for finding its two-terminal dc conductance. The latter is affected by the different nature of the charge carriers in the leads and in the wire.…”