Towers of Quantum Many-body Scars from Integrable Boundary States

Abstract

We construct several models with multiple quantum many-body scars (QMBS) using integrable boundary states (IBS). Specifically, we focus on the tilted Néel states, which are parametrized IBS for the spin-1/2 Heisenberg chain, and show that these states can be used to construct a tower of scar states. Our models exhibit periodic revival dynamics, showcasing a characteristic behavior of superpositions of QMBS. Furthermore, the tower of QMBS found in this study possesses a restricted spectrum generating algebra (RSGA) structure, indicating that QMBS are equally spaced in energy. This approach can be extended to two-dimensional models, which can be decomposed into an array of one-dimensional models. In this case, the tilted Néel states again serve as parent states for multiple scar states. These states demonstrate low entanglement entropy, marking them as exact scar states. Notably, their entanglement entropy adheres to the sub-volume law, further solidifying the nonthermal properties of QMBS. Our results provide novel insights into constructing QMBS using IBS, thereby illuminating the connection between QMBS and integrable models.

Figures (11)

• Figure 1: Level-spacing statistics in the middle half of the spectrum of $H_1(g, h_y)$ [Eq. \ref{['eq:ham']}] with $g = 1$, $h_y = 1$, and $L=16$. The coefficients $c_j$ are randomly chosen from $[-1, 1]$. The data are taken in the symmetry sector with $Y = 0$. The Wigner-Dyson (GUE) and Poisson distributions are shown for comparison.
• Figure 2: Half-chain EE $S_A$ as a function of energy $E$ for all eigenstates of $H_1(g=1, h_y=1)$ with $L=12$. The random coefficients $c_j$ are chosen from the interval $[-1, 1]$. The density of data points is color coded. The red solid circles indicate the scar states $\ket{{\Psi}_n}$ ($n=0,1,...,12$).
• Figure 3: Half-chain EE $S_A$ as a function of energy $E$ for all eigenstates of $H_2(g =1.0, h_y = 0.5)$ with $L=12$ and $(J_x, J_y, J_z) = (0.1, 0.5, 1.0)$. The random coefficients $c_j$ are drawn from the interval $[-1, 1]$. The density of data points is color coded. The red solid circles indicate the half-chain EE and eigenenergy of $\ket{{\Psi}_n}$ ($n=0,1,...,12$).
• Figure 4: Fidelity dynamics for the Hamiltonian $H_2(g = 1, h_y =1)$ [Eq. \ref{['eq:XYZ_H']}] with $(J_x, J_y, J_z) = (0.1, 0.5, 1.0)$ and $L=12$. Each $c_j$ is randomly chosen from $[-1, 1]$. Periodic revivals can be seen when the initial state is $\ket{\mathbb{Z}_2}$ (blue), whereas for $\ket{\mathbb{Z}_3}$ (orange) the fidelity decays rapidly to $0$.
• Figure 5: The time evolution of the correlation function $C_{r=5}^x(t)$ [Eq. \ref{['eq:correlation']}] for $\ket{\mathbb{Z}_2}$ (blue) and $\ket{\mathbb{Z}_3}$ (orange). The system size is $L=12$, and the parameters of Hamiltonian $H_2$ [Eq. \ref{['eq:XYZ_H']}] are $g = 1$, $h_y = 1$ and $(J_x, J_y, J_z)=(0.1, 0.5, 1.0)$. Each $c_j$ is drawn from $[-1, 1]$ randomly.

Theorems & Definitions (1)

• Theorem 1