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}

Highlights

  • With the rapid development of experimental techniques, with the advancement of stable and precisely adjustable ultrashort pulse laser technologies, and the improvement of detection methods, the real-time information with atomic scale and subpicosecond resolution can be obtained

  • The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in |Zk (k = 2, 3) state illustrate the essential physics of the PXP model

  • The many-body quantum scars and the associated constrained dynamics can be unveiled. This phenomenology is characterized by the fact that the dynamics is anomalously slow provided the initial state has a nonnegligible overlap with scarred states

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Summary

INTRODUCTION

With the rapid development of experimental techniques, with the advancement of stable and precisely adjustable ultrashort pulse laser technologies, and the improvement of detection methods, the real-time information with atomic scale and subpicosecond resolution can be obtained. Quantum scars are nonthermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the PXP model [16–19]. The underlying mechanism for the 51 Rydberg atoms finding the return journey of a specific initial state in the Hilbert space of more than 4 × 1010 dimensions is fuzzy Ergodicity breaking in such systems can often be attributed to the presence of symmetries (hidden, emergent, or explicit) that preclude the establishment of a global equilibrium state [23,24]. We study the spin-1 Kitaev chain, which is nonintegrable We show that this model after increasing spin to S = 1 surprisingly harbors an extensive set of anomalous scarred eigenstates at finite energy density that exhibit subextensive entanglement entropy. Thereby we are guided by the idea that studying a wide variety of interacting systems with exact scar states and their stability to perturbations would be beneficial for general understanding

SPIN-1 KITAEV CHAIN In the present paper, we focus on a spin-1 Kitaev chain
STABILITY OF QMBS AGAINST HEISENBERG INTERACTIONS
PHASE DIAGRAM OF THE KITAEV-HEISENBERG CHAIN FOR S = 1
SUMMARY AND CONCLUSION

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