Exotic topological order in fractal spin liquids

We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of string-like extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly-fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.Comment: 18 pages, 10 figure

Topological phases with generalized global symmetries

We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported on a $(d+1)$-colorable graph by using a family of unitary phase gates, known as multi-qubit control-$Z$ gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Non-triviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.Comment: 32 pages, 17 figures, single column (v2, corrected minor mistakes and typos, to appear in PRB

PENGARUH PENINGKATA N KEPERCAYAAN DIRI TERHADAP HASIL BELAJAR SISWA PADA MATA PRAKTEK TUNE UP MOTOR BENSIN DI SMK MUHAMMADYAH PRAMBANAN TAHUN AJARAN 2010/2011

Penelitian ini mempunyai bertujuan untuk mengetahui adanya: (1) pengaruh penggunaan peningkatan percaya diri terhadap hasil belajar siswa kelas 2 Jurusan Teknik Otomotif di SMK Muhammadiyah Prambanan, (2) Perbedaan hasil belajar siswa antara yang diberi peningkatan kepercayaan diri dengan yang tidak diberi kepercayaan diri pada siswa kelas siswa kelas 2 Jurusan Teknik Otomotif di SMK Muhammadiyah Prambanan. Subyek penelitian ini adalah siswa kelas 2 program keahlian teknik otomotif SMK Muhammadiyah Prambanan. Obyek penelitian yaitu hasil belajar siswa kelas 2 jurusan teknik otomotif pada mata praktek tune up motor bensin. Metode penelitian yang digunakan adalah quasi experimen designt. Desain yang digunakan penelitian ini adalah nonequivalent control group design. Pengumpulan data dalam penelitian ini menggunakan tes dan angket. Tes dan angket berupa pretest dan posttest yang diberikan pada kelompok eksperimen dan kelompok kontrol. Validitas instrumen dilakukan secara experts judgment.. Teknik analisis data yang digunakan adalah statistik deskriptif dan t-test dengan bantuan komputer program Microsoft office Excel 2007. Statistik deskriptif digunakan untuk mengetahui kecenderungan tingkat prestasi belajar siswa, sedangkan t-test digunakan untuk mengetahui perbedaaan tingkat hasil belajar sebelum dan sesudah menggunakan penngkatan percaya diri pada pembelajaran mata diklat praktek tune up motor bensin. Hasil penelitian menunjukkan bahwa : rerata kepercayaan diri post-test kelas eksperimen = 70,36, kepercayaan diri post-test kelas kontrol = 64,.36, serta rerata hasil belajar post-test kelas eksperimen = 73,75, post-test hasil belajar kelas kontrol = 68,61. Ada perbedaan kepercayaan diri antara kelas experimen dibanding kelas kontrol sebesar 4,45% serta perbedaan hasil belajar antara kelas experimen dibanding kelas kontrol sebesar 3,61%. Hasil uji t posttest kepercayaan diri sebesar 2,250 dan hasil belajar sebesar 1,689, jika dibanding dengan t tabel (1,689) dan di uji dengan uji pihak kanan maka t hitung > t tabel sehingga Ho di tolak dan Ha di terima, maka dapat disimpulkan bahwa ada pengaruh peningkatan kepercayaan diri terhadap hasil belajar

Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory

We examine two proposals for marginally self-correcting quantum memory, the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.Comment: 19 pages, 18 figure