Resonant Fields Inducing Energy Towers in Lieb Quantum Spin Lattice

TL;DR

This paper investigates how resonant staggered magnetic fields induce special energy states, called energy towers or quantum many-body scars, in a Lieb lattice modeled by the XXZ Heisenberg Hamiltonian, combining exact algebraic methods and numerical simulations.

Contribution

It introduces a restricted spectrum generating algebra (RSGA) approach to identify exact eigenstates and demonstrates the existence of quasi-RSGA states acting as energy towers in the Lieb lattice.

Findings

Exact eigenstates constructed via RSGA under resonant fields.

Identification of energy towers as quantum many-body scars.

Numerical evidence of quasi-RSGA states in low-lying spectrum.

Abstract

We study a ferromagnetic XXZ Heisenberg model on a Lieb lattice. A set of exact eigenstates is constructed based on the restricted spectrum generating algebra (RSGA) when a resonant staggered magnetic field is applied. These states are identical to the eigenstates of a system of two coupled angular momenta. Furthermore, we find that the RSGA can be applied to other eigenstates of the Lieb lattice in an approximate manner. Numerical simulations reveal that there exist sets of eigenstates, which obey a quasi-RSGA. These states act as energy towers within the low-lying excited spectrum, indicating that they are quantum many-body scars.