Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen
SciPost Phys. 14, 146 (2023) ·
published 7 June 2023

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We introduce a disorderfree model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two upspins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ringexchange 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 quasionedimensional 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 manybody scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the onedimensional PXP chain with open boundaries, a paradigmatic model for quantum manybody scarring; while the junction of two wires represents a distinct constrained model.
Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta
SciPost Phys. 14, 004 (2023) ·
published 16 January 2023

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$^{87}{\rm Rb}$ atoms are known to have longlived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf r}$ and ${\bf r'}$. Here we study such atoms in a twoleg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $\Delta$ and $\lambda$ respectively. We show that when $V_{{\bf r r'}} \gg(\ll) \Delta, \lambda$ for ${\bf r}{\bf r'}=1(>1)$, these ladders host a plateau for a wide range of $\lambda/\Delta$ where the ground states are selected by a quantum orderbydisorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density $1/4$. Our study further unravels the presence of an emergent Ising transition stabilized via the orderbydisorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning $\lambda_c/\Delta=1/3$ which agrees well with exactdiagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{{\bf r} {\bf r'}} = V_0 /{\bf r}{\bf r'}^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $\lambda_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.
SciPost Phys. 12, 148 (2022) ·
published 6 May 2022

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We demonstrate the presence of anomalous highenergy eigenstates, or manybody scars, in $U(1)$ quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic RokhsarKivelson 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 (offdiagonal) in the computational basis. Both these interacting models possess an exponentially large number of midspectrum 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.
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in Submissions  report on Strong Hilbert space fragmentation via emergent quantum drums in two dimensions