Phase diagram and sweep dynamics of a one-dimensional generalized cluster model

TL;DR

This study explores quantum phase transitions and dynamics in a one-dimensional generalized cluster model, revealing phase boundaries, topological degeneracies, and quasiparticle-induced periodic structures during parameter sweeps.

Contribution

It introduces a comprehensive numerical analysis of phase boundaries, entanglement properties, and dynamical behavior in a generalized 1D cluster model with multiple interactions.

Findings

Identified phase boundaries using energy gaps and order parameters.

Linked entanglement spectrum degeneracies to ground state degeneracies.

Observed spatially periodic structures in correlations after slow parameter sweeps.

Abstract

We numerically study quantum phase transitions and dynamical properties in the one-dimensional cluster model with several interactions by using the time-evolving block decimation method for infinite systems and the exact diagonalization. First, boundaries among several quantum phases of the model are determined from energy gap and each phase is characterized by order parameters and the entanglement spectrum (ES). We confirm that in the model with open boundary condition the degeneracy of the lowest levels in the ES corresponds to that of the ground states. Then, using the time-dependent Bogoliubov transformation with open boundary condition, we investigate dynamical properties during an interaction sweep through the critical point which separates two topological phases involving four-fold degeneracy in the ground state. After a slow sweep across the critical point, we observe spatially periodic structures in the string correlation functions and the entanglement entropy. It is shown that the periodicities stem from the Bogoliubov quasiparticles generated near the critical point.