Quantum Many-Body Scars in Spin-1 Kitaev Chains

TL;DR

This paper investigates quantum many-body scars in the spin-1 Kitaev chain, revealing their stability, connection to PXP models, and the rich phase diagram including symmetry-broken and spin liquid phases.

Contribution

It provides the first detailed analysis of quantum scars in the spin-1 Kitaev chain, linking them to PXP Hamiltonian embeddings and exploring phase transitions with advanced numerical methods.

Findings

Quantum scars are embedded in the spin-1 Kitaev chain spectrum.

The phase diagram includes symmetry-broken and spin liquid phases.

Scar stability depends on the type of perturbations, especially $ ext{Z}_2$-symmetry-preserving ones.

Abstract

To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $\vert\mathbb{Z}_k\rangle$ ($k=2,3$) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\phi$, where the Kitaev term is $K\equiv\sin(\phi)$ and competes with the Heisenberg $J\equiv\cos(\phi)$ term. One finds a rich ground state phase diagram as a function of the angle $\phi$. Depending on the ratio $K/J\equiv\tan(\phi)$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey $\mathbb{Z}_2$-symmetry, while it becomes unstable against Heisenberg-type perturbations.\\ \textit{Accepted for publication in Physical Review Research}