## Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models

Saptarshi Biswas, Debasish Banerjee, Arnab Sen

SciPost Phys. 12, 148 (2022) · published 6 May 2022

- doi: 10.21468/SciPostPhys.12.5.148
- Submissions/Reports

### Abstract

We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in $U(1)$ quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian $H=\mathcal{O}_{\mathrm{kin}} + \lambda \mathcal{O}_{\mathrm{pot}}$ where $\mathcal{O}_{\mathrm{pot}}$ ($\mathcal{O}_{\mathrm{kin}}$) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at $\lambda=0$ that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for $|\lambda| \lesssim \mathcal{O}(1)$ both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite $\lambda$ show a rich variety with those that are composed solely from the zero modes of $\mathcal{O}_{\mathrm{kin}}$, those that contain an admixture of both the zero and the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$, and finally those composed solely from the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$. We give analytic expressions for certain "lego scars" for the quantum dimer model on rectangular lattices where one of the linear dimensions can be made arbitrarily large, with the building blocks (legos) being composed of emergent singlets and other more complicated entangled structures.

### Cited by 22

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Saptarshi Biswas, -
^{3}^{4}Debasish Banerjee, -
^{5}Arnab Sen

^{1}Northwestern University [NUS]^{2}भारतीय विज्ञान शिक्षा और अनुसंधान संस्थान, कोलकाता / Indian Institute of Science Education and Research Kolkata [IISER]^{3}Saha Institute of Nuclear Physics [SINP]^{4}होमी भाभा राष्ट्रीय संस्थान / Homi Bhabha National Institute [HBNI]^{5}ইন্ডিয়ান অ্যাসোসিয়েশন ফর দ্য কালটিভেশন অফ সায়েন্স / Indian Association for the Cultivation of Science [IACS]