Enriching the dynamical phase diagram of spin chains with long-range interactions

Jad C. Halimeh, Valentin Zauner-Stauber

Published 2016-10-06Version 1

Using an infinite matrix product state technique (iMPS) based on the time-dependent variational principle, we study two major types of dynamical phase transition (DPT) in the transverse-field Ising model with long-range power-law ($\propto1/r^{\alpha}$ with $r$ inter-spin distance) interactions in the thermodynamic limit -- \textit{type-I}: based on order parameters in a (quasi-)steady state, and \textit{type-II}: based on nonanalyticities (cusps) in the Loschmidt-echo return rate. We construct the corresponding rich dynamical phase diagram, whilst considering different quench initial conditions. We find a nontrivial connection between both types of DPT based on their critical lines. Moreover, we observe a new type-II dynamical phase in a certain range of interaction exponent $\alpha$, characterized by what we call \textit{anomalous cusps}, which are distinct from the regular cusps usually associated with a type-II DPT. We illustrate the transition between these two groups of cusps through the rate-function branches of the iMPS transfer matrix, which is a major strength of this method for studying the type-II DPT. Our results provide the characterization of experimentally-accessible signatures of the dynamical phases studied in this work.