Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics

TL;DR

This work develops a systematic method to construct asymptotic quantum many-body scar (AQMBS) states by embedding scar towers into a parent Hamiltonian and exploiting a restricted spectrum generating algebra (RSGA). The approach relies on a tripartite Hamiltonian form and a carefully defined Hilbert subspace where AQMBS arise as low-lying gapless excitations of a positive semidefinite parent Hamiltonian, with a deep link to supersymmetric quantum mechanics in which the QMBS states are SUSY unbroken ground states. The framework is then applied to multiple 1D models (Spin-1 XY, Fermi-Hubbard with correlated hopping, DH, domain-wall conserving, Onsager scar, and nonmaximal spin scar models), yielding explicit scar operators, explicit energy spectra, and evidence of subvolume entanglement for the AQMBS, as well as occasional perfect revivals. Collectively, the results unify QMBS and AQMBS constructions within a SUSY QM perspective and clarify how AQMBS can be systematically engineered via the spectrum of a parent Hamiltonian, with implications for understanding nonergodic dynamics in realistic many-body systems.

Abstract

We develop a systematic method for constructing asymptotic quantum many-body scar (AQMBS) states. While AQMBS states are closely related to quantum many-body scar (QMBS) states, they exhibit key differences. Unlike QMBS states, AQMBS states are not energy eigenstates of the Hamiltonian, making their construction more challenging. We demonstrate that, under appropriate conditions, AQMBS states can be obtained as low-lying gapless excited states of a parent Hamiltonian, which has a QMBS state as its ground state. Furthermore, our formalism reveals a connection between QMBS and supersymmetric (SUSY) quantum mechanics. The QMBS state can be interpreted as a SUSY-unbroken ground state.

Figures (3)

• Figure 1: Schematic of Hilbert subspaces introduced in this paper. The region surrounded by the red solid and the blue solid line represents $\mathcal{H}_P$ and $\mathcal{H}_{\rm scar}$, respectively. The colored region represents $\mathcal{H}_{\rm thermal}=\mathcal{H}_{\rm scar}^{\perp}$. The AQMBS states belong to $\mathcal{H}_P\setminus \mathcal{H}_{\rm scar}$.
• Figure 2: Difference of the energy variance $\Delta (\Delta E^2_n)=\widetilde{\Delta E^2_n}-\Delta E_n^2$ as a function of the system size for several $n$. Here, we fix $l=1$ in Eq. (\ref{['eq:energy_variance_AQMBS_DH_model']}).
• Figure 3: Half-chain von Neumann EE $S_{\rm vN}$ of AQMBS in the DH model (red circles) and the Onsager scar model (blue triangles). Here, we fix $l = 1$ for both models and choose $n = \lfloor M/4 \rfloor + 1$ for the DH model and $n = \lfloor M/4 \rfloor - 1$ for the Onsager scar model, where $\lfloor \cdot \rfloor$ denotes the floor function. The solid green line represents $(1/2)\ln(M) + 1/20$ for a guide to the eye.