Dynamical correlation functions of a two-spin operator in quantum spin chains

Jan de Gier

We consider the paper 'Adjacent spin operator dynamical structure factor of the S = 1/2 Heisenberg chain', by Klauser, Mossel and Caux (2012 J. Stat. Mech. P03012) to be a new and important step in the numerical analysis of the correlation functions of quantum spin chains. The correlation functions considered in this paper were not previously computed, their analytical study is extremely complicated and the numerical results can be used for comparison with experiments.

Gerhard Müller, H. Beck

Rodrigo G. Pereira, Steven White, Ian K. Affleck

Frank Göhmann, Karol Kajetan Kozlowski, Junji Suzuki

We analyze 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.

Davide Rossini, Sei Suzuki, Giuseppe Mussardo +2 more

We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior; i.e., they decay exponentially to zero with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasiparticles of the model: nonlocal operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analyzing their robustness with respect to a sufficiently strong integrability-breaking term.

Minoru Takahashi, Masahiro Shiroishi