Local stabilizer codes in three dimensions without string logical operators

Haah, Jeongwan

doi:10.1103/physreva.83.042330

Cited by 630 publications

(887 citation statements)

References 25 publications

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“…Certainly, there are limits to what can be realized in field theory: for example, as is familiar to condensed matter physicists, not every lattice model has a continuum limit. An example is given by the Haah code [2], one of the "quantum solids" mentioned above, in which the jump in the ground state degeneracy between an even and an odd number of lattice sites is expected to preclude a continuum description. It is therefore natural to assume that the phases of matter describable by local field theory are highly restricted.…”

Section: Jhep10(2017)081mentioning

confidence: 99%

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Instantons and entanglement entropy

Bhattacharyya

Hung

Melby-Thompson

2017

J. High Energ. Phys.

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Abstract:We would like to put the area law -believed to be obeyed by entanglement entropies in the ground state of a local field theory -to scrutiny in the presence of nonperturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton contributions are well understood, including U(1) gauge theory in 2+1 dimensions and false vacuum decay in φ 4 theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.

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Section: Jhep10(2017)081mentioning

confidence: 99%

“…The same considerations apply there. 2 As opposed to a theory with gauge group R: compactness is important here.…”

Section: Free U(1) Gauge Theory In D = 3 and The Xy Modelmentioning

confidence: 99%

Instantons and entanglement entropy

Bhattacharyya

Hung

Melby-Thompson

2017

J. High Energ. Phys.

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“…Most results for self-correcting quantum memories in 2-d and 3-d to date have been negative [4][5][6] or use operators of unbounded strength [7]. One exception has been the cubic code [8], but that too has an energy barrier of only log(L). In this letter, we improve the best known energy barrier for spin Hamiltonians with topological order from O(log L) to O(L 2/3 ).…”

Section: Introductionmentioning

confidence: 99%

3D Topological Quantum Memory with a Power-Law Energy Barrier

Michnicki

2014

Phys. Rev. Lett.

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We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3-d version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting code is a [[O(L 3 3 )]] stabilizer code with an energy barrier of O(L 2 3 ), which is an exponential improvement over the previous highest energy barrier in 3-d. No-go results are avoided by breaking microscopic translation invariance.

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“…15 Yet, in some cases, quantum spin liquids may exhibit topological order that is beyond description of TQFT. For example, in three spatial dimensions, the cubic code, recently proposed by Haah,16 possesses topological order with stability against local perturbations, but are completely different from conventional topological spin liquids. For one thing, the number of degenerate ground states is exponential in the linear length of the lattice.…”

Section: Introductionmentioning

confidence: 99%

Exotic topological order in fractal spin liquids

2013

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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 stringlike 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.

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Local stabilizer codes in three dimensions without string logical operators

Cited by 630 publications

References 25 publications

Instantons and entanglement entropy

Instantons and entanglement entropy

3D Topological Quantum Memory with a Power-Law Energy Barrier

Exotic topological order in fractal spin liquids

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