Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
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2023
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| author | Sau, Indrajit Stornati, Paolo Banerjee, Debasish Sen, Arnab |
| author_facet | Sau, Indrajit Stornati, Paolo Banerjee, Debasish Sen, Arnab |
| contents | 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 $H = \mathcal{O}_{\mathrm{kin}} + λ\mathcal{O}_{\mathrm{pot}}$, where $λ$ 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, $|ψ_s \rangle$, which satisfy $\mathcal{O}_{\mathrm{pot},\square} |ψ_s\rangle = |ψ_s\rangle$ for all elementary plaquettes on one sublattice and $ \mathcal{O}_{\mathrm{pot},\square} | ψ_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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_06773 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories Sau, Indrajit Stornati, Paolo Banerjee, Debasish Sen, Arnab High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics 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 $H = \mathcal{O}_{\mathrm{kin}} + λ\mathcal{O}_{\mathrm{pot}}$, where $λ$ 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, $|ψ_s \rangle$, which satisfy $\mathcal{O}_{\mathrm{pot},\square} |ψ_s\rangle = |ψ_s\rangle$ for all elementary plaquettes on one sublattice and $ \mathcal{O}_{\mathrm{pot},\square} | ψ_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. |
| title | Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2311.06773 |