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Register a new userDeformed Symmetry Structures and Quantum Many-body Scar Subspaces
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A quantum many-body scar system usually contains a special non-thermal subspace (approximately) decoupled from the rest of the Hilbert space. In this work, we propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars, which are irreducible sectors of simple Lie groups transformed by matrix-product operators (or projected entangled pair operators), of which the entanglement entropies are proved to obey sub-volume-law scaling and thus violate the eigenstate thermalization hypothesis. A deformed symmetric space, in general, is required to have at least a U(1) sub-Lie-group symmetry to allow coherent periodic dynamics from certain low-entangled initial states. We enumerate several possible deforming transformations based on the sub-group symmetry requirement and recover many existing models whose scar states are not connected by symmetry. In particular, a two-dimensional scar model is proposed, which hosts a periodic dynamical trajectory on which all states are topologically ordered.
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We construct a set of exact, highly excited eigenstates for a nonintegrable spin-1/2 model in one dimension that is relevant to experiments on Rydberg atoms in the antiblockade regime. These states provide a new solvable example of quantum many-body scars: their sub-volume-law entanglement and equal energy spacing allow for infinitely long-lived coherent oscillations of local observables following a suitable quantum quench. While previous works on scars have interpreted such oscillations in terms of the precession of an emergent macroscopic SU(2) spin, the present model evades this description due to a set of emergent kinetic constraints in the scarred eigenstates that are absent in the underlying Hamiltonian. We also analyze the set of initial states that give rise to periodic revivals, which persist as approximate revivals on a finite timescale when the underlying model is perturbed. Remarkably, a subset of these initial states coincides with the family of area-law entangled Rokhsar-Kivelson states shown by Lesanovsky to be exact ground states for a class of models relevant to experiments on Rydberg-blockaded atomic lattices.
We find exponentially many exact quantum many-body scar states in a two-dimensional PXP model -- an effective model for a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. Such scar states are remarkably simple valence bond solids despite being at effectively infinite temperature, and thus strongly violate the eigenstate thermalization hypothesis. Given a particular boundary condition, such eigenstates have integer-valued energies. Moreover, certain charge-density-wave initial states give rise to strong oscillations in the Rydberg excitation density after a quantum quench and tower-like structures in their overlaps with eigenstates.
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing positivity constraints on certain operator expectation values. Complemented with variational upper bounds, ground state observables are constrained to be within a narrow range. The method is demonstrated with the Hubbard model in one and two dimensions, and bounds on ground state double occupancy and magnetization are discussed.
Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower-bounds the thermalization time for any scar state as $t^{*} sim O(lambda^{-1/(1+d)})$, where $d$ is the spatial dimension of the system and $lambda$ is the perturbation strength.
We study the spin-1 XY model on a hypercubic lattice in $d$ dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. Namely, they exhibit subextensive entanglement entropy and spatiotemporal long-range order, both believed to be impossible in typical highly excited eigenstates of nonintegrable quantum many-body systems. While generic initial states are expected to thermalize, we show analytically that the eigenstates we construct lead to weak ergodicity breaking in the form of persistent oscillations of local observables following certain quantum quenches--in other words, these eigenstates provide an archetypal example of so-called quantum many-body scars. This work opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena.
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