Dynamical phase diagram of spin chains with long-range interactions

TL;DR

This paper investigates the dynamical phase transitions in long-range interacting spin chains using advanced numerical methods, revealing a new phase characterized by anomalous cusps and establishing connections between different types of transitions.

Contribution

The study introduces a comprehensive dynamical phase diagram for long-range transverse-field Ising models, discovering a novel DPT-II phase with anomalous cusps and linking it to DPT-I.

Findings

Identification of a new DPT-II phase with anomalous cusps

Establishment of a connection between DPT-I and DPT-II critical lines

Construction of a detailed dynamical phase diagram for long-range interactions

Abstract

Using an infinite Matrix Product State (iMPS) technique based on the time-dependent variational principle (TDVP), we study two major types of dynamical phase transitions (DPT) in the one-dimensional transverse-field Ising model (TFIM) with long-range power-law ($\propto1/r^{\alpha}$ with $r$ inter-spin distance) interactions out of equilibrium in the thermodynamic limit -- \textit{DPT-I}: based on an order parameter in a (quasi-)steady state, and \textit{DPT-II}: based on non-analyticities (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, and very interestingly, we detect a new DPT-II dynamical phase in a certain range of interaction exponent $\alpha$, characterized by what we call \textit{anomalous cusps} that are distinct from the \textit{regular cusps} usually associated with DPT-II. Our results provide the characterization of experimentally accessible signatures of the dynamical phases studied in this work.