Out-of-time-ordered correlators in Luttinger liquids

Rövid cím: 
Out-of-time-ordered correlators in Luttinger
2018. 09. 14. 10:15
BME Fizikai Intézet, Elméleti Fizika Tanszék, Budafoki út 8. F-épület, III lépcsőház, szemináriumi szoba
Balázs Dóra (BUTE Dept. Theor. Phys.)

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behaviour combining robustly universal and non-universal features. For the short
wavelength density operator, out-of-time-ordered commutators reach a sizeable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. We benchmark our findings numerically on an interacting spinless fermion model in 1D, and find persistence of central features even in the non-integrable case. As a non-universal feature, the short time growth exhibits a distance dependent power.