Construction of asymptotic quantum many-body scar states in the SU($N$) Hubbard model

TL;DR

The paper addresses constructing asymptotic quantum many-body scars (AQMBS) in nonintegrable quantum systems by extending the RSGA framework to SU($N$) Hubbard chains with $N\ge 3$ and embedding the scar subspace into an enlarged subspace $\mathcal{H}_P$. It develops a multi-ladder RSGA (MLRSGA) and a symmetry-based Hamiltonian decomposition to implement a systematic parent-Hamiltonian construction, identifying the SU($N$) ferromagnetic Heisenberg model as the parent Hamiltonian. The resulting gapless magnon excitations provide explicit AQMBS that are orthogonal to the scar tower, have vanishing energy variance in the thermodynamic limit, and exhibit subvolume entanglement bounded via MPS/MPO methods. This work broadens the family of parent-Hamiltonian constructions beyond spin-1/2 and reveals analytic, low-entanglement excitations in SU($N$)-symmetric systems with potential routes toward experimental realization.

Abstract

We construct asymptotic quantum many-body scars (AQMBS) in one-dimensional SU($N$) Hubbard chains ($N\geq 3$) by embedding the scar subspace into an auxiliary Hilbert subspace $\mathcal{H}_P$ and identifying a parent Hamiltonian within it, together with a corresponding extension of the restricted spectrum-generating algebra to the multi-ladder case. Unlike previous applications of the parent-Hamiltonian scheme, we show that the parent Hamiltonian becomes the SU($N$) ferromagnetic Heisenberg model rather than the spin-1/2 case, so that its gapless magnons realize explicit AQMBS of the original model. Working in the doublon-holon subspace, we derive this mapping, obtain the one-magnon dispersion for periodic and open boundaries, and prove (i) orthogonality to the tower of scar states, (ii) vanishing energy variance in the thermodynamic limit, and (iii) subvolume entanglement entropy with rigorous MPS/MPO bounds. Our results broaden the parent-Hamiltonian family for AQMBS beyond spin-1/2 and provide analytic, low-entanglement excitations in SU($N$)-symmetric systems.

Theorems & Definitions (4)

• Lemma 1: Spectrum generating algebra (SGA)
• Lemma 2: RSGA-1
• Lemma 3: RSGA-$m$
• proof : Proof of Eq. \ref{['eq:energy_tower']}