Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories

• URL: http://arxiv.org/abs/2311.06773v1
• Date: Sun, 12 Nov 2023 08:32:00 GMT
• Title: Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
• Authors: Indrajit Sau, Paolo Stornati, Debasish Banerjee, Arnab Sen
• Abstract summary: We elucidate the structure and properties of a class of anomalous high-energy states of matter-free $U(1)$ quantum link gauge theory Hamiltonians. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free $U(1)$ quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is $H = \mathcal{O}_{\mathrm{kin}} + \lambda \mathcal{O}_{\mathrm{pot}}$, where $\lambda$ is a real-valued coupling, and $\mathcal{O}_{\mathrm{kin}}$ ($\mathcal{O}_{\mathrm{pot}}$) are summed local diagonal (off-diagonal) operators in the electric flux basis acting on the elementary plaquette $\square$. The spectrum of the model in its spin-$\frac{1}{2}$ representation on $L_x \times L_y$ lattices reveal the existence of sublattice scars, $|\psi_s \rangle$, which satisfy $\mathcal{O}_{\mathrm{pot},\square} |\psi_s\rangle = |\psi_s\rangle$ for all elementary plaquettes on one sublattice and $ \mathcal{O}_{\mathrm{pot},\square} | \psi_s \rangle =0 $ on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of $\mathcal{O}_{\mathrm{kin}}$. We demonstrate a ``triangle relation'' connecting the sublattice scars with nonzero integer eigenvalues of $ \mathcal{O}_{\mathrm{kin}} $ to particular sublattice scars with $\mathcal{O}_{\mathrm{kin}} = 0$ eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of $ \mathcal{O}_{\mathrm{kin}} $ become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another $U(1)$ quantum link model with a staggered short-ranged diagonal term.

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