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Register a new userTopological Quantum Many-Body Scars in Quantum Dimer Models on the Kagome Lattice
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We utilize a general strategy to turn classes of frustration free lattice models into similar classes containing quantum many-body scars within the bulk of their spectrum while preserving much or all of the original symmetry. We apply this strategy to a well-known class of quantum dimer models on the kagome lattice with a large parameter space. We discuss that the properties of the resulting scar state(s), including entanglement entropy, are analytically accessible. Settling on a particular representative within this class of models retaining full translational symmetry, we present numerical exact diagonalization studies on lattices of up to 60 sites, giving evidence that non-scar states conform to the eigenstate thermalization hypothesis. We demonstrate that bulk energies surrounding the scar are distributed according to the Gaussian ensemble expected of their respective symmetry sector. We further contrast entanglement properties of the scar state with that of all other eigenstates.
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Certain wave functions of non-interacting quantum chaotic systems can exhibit scars in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.
We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $ u = 1/3$, the model exactly maps onto the so-called PXP model, a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors $ u = p/(2p+1)$, and show that the model is equivalent to non-integrable spin-chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.
We revisit the $eta$-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. $eta$-pairing occurs due to an algebraic structure known as a Spectrum Generating Algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original $eta$-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a Restricted Spectrum Generating Algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a sub-thermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the AKLT model.
We construct few-body, interacting, nonlocal Hamiltonians with a quantum scar state in an otherwise thermalizing many-body spectrum. In one dimension, the embedded state is a critical state, and in two dimensions, the embedded state is a chiral topologically ordered state. The models are defined on slightly disordered lattices, and the scar state appears independent of the precise realization of the disorder. A parameter allows the scar state to be placed at any position in the spectrum. We show that the level spacing distributions are Wigner-Dyson and that the entanglement entropies of the states in the middle of the spectrum are close to the Page value. Finally, we confirm the topological order in the scar state by showing that one can insert anyons into the state.
In this letter, we study the PXP Hamiltonian with an external magnetic field that exhibits both quantum scar states and quantum criticality. It is known that this model hosts a series of quantum many-body scar states violating quantum thermalization at zero magnetic field, and it also exhibits an Ising quantum phase transition driven by finite magnetic field. Although the former involves the properties of generic excited states and the latter concerns the low-energy physics, we discover two surprising connections between them, inspired by the observation that both states possess log-volume law entanglement entropies. First, we show that the quantum many-body scar states can be tracked to a set of quantum critical states, whose nature can be understood as pair-wisely occupied Fermi sea states. Second, we show that the partial violation of quantum thermalization diminishes in the quantum critical regime. We envision that these connections can be extended to general situations and readily verified in existing cold atom experimental platforms.
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