Tower of quantum scars in a partially many-body localized system

Isolated quantum many-body systems are often well-described by the eigenstate thermalization hypothesis. There are, however, mechanisms that cause different behavior: many-body localization and quantum many-body scars. Here, we show how one can find disordered Hamiltonians hosting a tower of scars by adapting a known method for finding parent Hamiltonians. Using this method, we construct a spin-1/2 model which is both partially localized and contains scars. We demonstrate that the model is partially localized by studying numerically the level spacing statistics and bipartite entanglement entropy. As disorder is introduced, the adjacent gap ratio transitions from the Gaussian orthogonal ensemble to the Poisson distribution and the entropy shifts from volume-law to area-law scaling. We investigate the properties of scars in a partially localized background and compare with a thermal background. At strong disorder, states initialized inside or outside the scar subspace display different dynamical behavior but have similar entanglement entropy and Schmidt gap. We demonstrate that localization stabilizes scar revivals of initial states with support both inside and outside the scar subspace. Finally, we show how strong disorder introduces additional approximate towers of eigenstates.Comment: 18 pages, 12 figures, v2: accepted versio

Relation between two measures of entanglement in spin-1/2 and spinless fermion quantum chain systems

The concepts of concurrence and mode concurrence are the measures of entanglement for spin-1/2 and spinless fermion systems respectively. Based on the Jordan-Wigner transformation, any spin-1/2 system is always associated with a fermion system (called counterpart system). The comparison of concurrence and mode concurrence can be made with the aid of the Marshall's sign rule for the ground states of spin-1/2 $XXZ$ and spinless fermion chain systems. We observe that there exists an inequality between concurrence and mode concurrence for the ground states of the two corresponding systems. The spin-1/2 XY chain system and its spinless fermion counterpart as a realistic example is discussed to demonstrate the analytical results.Comment: 7 pages, no figures, publication version, to appear in PR

Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals

Recently, it was shown that fractional quantum Hall states can be defined on fractal lattices. Proposed exact parent Hamiltonians for these states are nonlocal and contain three-site terms. In this work, we look for simpler, approximate parent Hamiltonians for bosonic Laughlin states at half filling, which contain only onsite potentials and two-site hopping with the interaction generated implicitly by hardcore constraints (as in the Hofstadter and Kapit-Mueller models on periodic lattices). We use an ``inverse method'' to determine such Hamiltonians on finite-generation Sierpi\'{n}ski carpet and triangle lattices. The ground states of some of the resulting models display relatively high overlap with the model states if up to third neighbor hopping terms are considered, and by increasing the maximum hopping distance one can achieve nearly perfect overlaps. When the number of particles is reduced and additional potentials are introduced to trap quasiholes, the overlap with a model quasihole wavefunction is also high in some cases, especially for the nonlocal Hamiltonians. We also study how the small system size affects the braiding properties for the model quasihole wavefunctions and perform analogous computations for Hamiltonian models.Comment: Version accepted in Phys. Rev. A. See the Ancillary Files for the Supplementary Materia

The politics of corporate responsibility: CSR and the governance of child labor and core labor rights in the 1990s

‘No amount of preparation could have lessened the shock and revulsion I felt on entering a sporting-goods factory in the town of Sialkot, seventy miles from Lahore, where scores of children, most of them aged five to ten, produce soccer balls by hand for forty rupees, or about $1.20, a day. The children work eighty hours a week in near-total darkness and total silence. According to the foreman, the darkness is both an economy and a precautionary measure; child-rights activists have difficulty taking photographs and gathering evidence of wrongdoing if the lighting is poor. The silence is to ensure product quality: "If the children speak, they are not giving their complete attention to the product and are liable to make errors.” The children are permitted one thirty-minute meal break each day; they are punished if they take longer. They are also punished if they fall asleep, if their workbenches are sloppy, if they waste material or miscut a pattern, if they complain of mistreatment to their parents or speak to strangers outside the factory. A partial list of "infractions” for which they may be punished is tacked to a wall near the entrance. It’s a document of dubious utility: the children are illiterate. Punishments are doled out in a storage closet at the rear of the factory. There, amid bales of wadding and leather, children are hung upside down by their knees, starved, caned, or lashed.