We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian H=O_{kin}+λO_{pot}, where O_{pot} (O_{kin}) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero λ but some special linear combinations that simultaneously diagonalize O_{kin} and O_{pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.
We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian H=O_{kin}+λO_{pot}, where O_{pot} (O_{kin}) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero λ but some special linear combinations that simultaneously diagonalize O_{kin} and O_{pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.
We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 quantum spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of non-ergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge-invariant. In our case, the Hamiltonian H=Okin+λOpot, where Opot (Okin) is diagonal (off-diagonal) in the electric flux basis, contains exact mid-spectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any non-zero λ but some special linear combinations that simultaneously diagonalize Okin and Opot survive as quantum many-body scars, suggesting an order-by-disorder mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on ladders with up to 56 spins, which may be tested using available proposals of quantum simulators.
Scars from protected zero modes and beyond in U(1) quantum link and quantum dimer models
We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in U(1) 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}} H = 𝒪 k i n + λ 𝒪 p o t where \mathcal{O}_{\mathrm{pot}} 𝒪 p o t ( \mathcal{O}_{\mathrm{kin}} 𝒪 k i n ) 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 λ = 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) | λ | ≲ 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 λ show a rich variety with those that are composed solely from the zero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n , those that contain an admixture of both the zero and the nonzero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n , and finally those composed solely from the nonzero modes of \mathcal{O}_{\mathrm{kin}} 𝒪 k i n
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=Okin+λOpot , where λ is a real-valued coupling, and Okin ( Opot ) are summed local off-diagonal (diagonal) operators in the electric flux basis acting on the elementary plaquette □ . The spectrum of the model in its spin- 12 representation on Lx×Ly lattices reveal the existence of sublattice scars, |ψs⟩ , which satisfy Opot,□|ψs⟩=|ψs⟩ for all elementary plaquettes on one sublattice and Opot,□|ψs⟩=0 on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of Okin . We demonstrate a “triangle relation” connecting the sublattice scars with nonzero integer eigenvalues of Okin to particular sublattice scars with Okin=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 Okin 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. Published by the American Physical Society 2024
Exact stabilizer scars in two-dimensional U(1) lattice gauge theory
The complexity of highly excited eigenstates is a central theme in nonequilibrium many-body physics, underpining questions of thermalization, classical simulability, and quantum information structure. In this work, considering the paradigmatic Rokhsar-Kivelson model, we connect quantum many-body scarring in Abelian lattice gauge theories to an emergent stabilizer structure. We identify a distinct class of scarred eigenstates, termed sublattice scars, originating from gauge-invariant zero modes that form exact stabilizer states. Remarkably, although the underlying Hamiltonian is not a stabilizer Hamiltonian, its eigenspectrum intrinsically hosts exact stabilizer eigenstates. These sublattice scars exhibit vanishing stabilizer Rényi entropy together with finite, highly structured entanglement, enabling efficient classical simulation. Exploiting their stabilizer structure, we construct explicit Clifford circuits that prepare these states in a two-dimensional lattice gauge model. Our results demonstrate that the scarred subspace of the Rokhsar-Kivelson spectrum forms an intrinsic stabilizer manifold, revealing a direct connection between stabilizer quantum information, lattice gauge constraints, and quantum many-body scarring.
We demonstrate that the kinematically constrained model of Rydberg atoms on a two-leg ladder with staggered detuning, $\mathrm{\ensuremath{\Delta}}\ensuremath{\in}[0,1]$, has quantum many-body scars (QMBSs) in its spectrum and represents a nonperturbative generalization of the paradigmatic PXP model defined on a chain. We show that these QMBSs result in coherent many-body revivals and site-dependent magnetization dynamics for both N\'eel and Rydberg vacuum initial states around $\mathrm{\ensuremath{\Delta}}=1$. The latter feature leads to eigenstate thermalization hypothesis (ETH)-violating finite imbalance at long times in a disorder-free system. This is further demonstrated by constructing appropriate local imbalance operators that display nonzero long-time averages for N\'eel and vacuum initial states. We also study the fidelity and Shannon entropy for such dynamics which, along with the presence of long-time finite imbalance, brings out the qualitatively different nature of QMBSs in PXP ladders with $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}1$ from those in the PXP chain. Finally, we identify additional exact midspectrum zero modes that stay unchanged as a function of $\mathrm{\ensuremath{\Delta}}$ and violate ETH.
Quantum many-body scarring is a paradigm of weak ergodicity breaking arising due to the presence of special nonthermal many-body eigenstates that possess low entanglement entropy, are equally spaced in energy, and concentrate in certain parts of the Hilbert space. Though scars have been shown to be intimately connected to gauge theories, their stability in such experimentally relevant models is still an open question, and it is generally considered that they exist only under fine-tuned conditions. In this work, we show through Krylov-based time-evolution methods how quantum many-body scars can be made robust in the presence of experimental errors through utilizing terms linear in the gauge-symmetry generator or a simplified pseudogenerator in U(1) and Z2 lattice gauge theories. Our findings are explained by the concept of quantum Zeno dynamics. Our experimentally feasible methods can be readily implemented in existing large-scale ultracold-atom quantum simulators and setups of Rydberg atoms with optical tweezers.