We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.
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- 1 ইন্ডিয়ান অ্যাসোসিয়েশন ফর দ্য কালটিভেশন অফ সায়েন্স / Indian Association for the Cultivation of Science [IACS]
- 2 रामकृष्ण मिशन विवेकानंद विश्वविद्यालय / Ramakrishna Mission Vivekananda University
- 3 University College London [UCL]
- Department of Science and Technology, Ministry of Science and Technology (through Organization: विज्ञान एवं प्रौद्योगिकी विभाग / Department of Science and Technology [DST])
- Horizon 2020 (through Organization: European Commission [EC])