Toy model of boundary states with spurious topological entanglement entropy

Kato, Kohtaro; Brandão, Fernando G. S. L.

doi:10.1103/physrevresearch.2.032005

Cited by 13 publications

(4 citation statements)

References 24 publications

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“…In a majority of known cases (see Ref. [55] for a possible counterexample), this is due to the presence of lower-dimensional SPT order around the boundary of the bipartition, which can in turn be related to the presence of SSPT order [18]. In fact, it was shown in Ref.…”

Section: Summary Of Resultsmentioning

confidence: 96%

“…The TEE refers to a constant correction to the area law when computing bipartite entanglement entropy, and is a topological invariant, in the sense that it takes a uniform value within a given topological phase of matter [49,50]. Recently, it has been understood that there are certain quantum states for which the TEE, for certain bipartitions, does not match the expected value [18,20,22,[51][52][53][54][55]. In a majority of known cases (see Ref.…”

Section: Summary Of Resultsmentioning

confidence: 99%

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Subsystem symmetry enriched topological order in three dimensions

Stephen

Garre-Rubio

Dua

et al. 2020

Phys. Rev. Research

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We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. The model is constructed starting from the 3D toric code, whose ground state can be viewed as an equal-weight superposition of two-dimensional (2D) membrane coverings. We then decorate those membranes with 2D cluster states possessing symmetry-protected topological order under linelike subsystem symmetries. This endows the decorated model with planar subsystem symmetries under which the looplike excitations of the toric code fractionalize, resulting in an extensive degeneracy per unit length of the excitation. We also show that the value of the topological entanglement entropy is larger than that of the toric code for certain bipartitions due to the subsystem symmetry enrichment. Our model can be obtained by gauging the global symmetry of a short-range entangled model which has symmetry-protected topological order coming from an interplay of global and subsystem symmetries. We study the nontrivial action of the symmetries on boundary of this model, uncovering a mixed boundary anomaly between global and subsystem symmetries. To further study this interplay, we consider gauging several different subgroups of the total symmetry. The resulting network of models, which includes models with fracton topological order, showcases more of the possible types of subsystem symmetry enrichment that can occur in 3D.

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Section: Summary Of Resultsmentioning

confidence: 96%

Section: Summary Of Resultsmentioning

confidence: 99%

Subsystem symmetry enriched topological order in three dimensions

Stephen

Garre-Rubio

Dua

et al. 2020

Phys. Rev. Research

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show abstract

“…Conversely, a boundary that gives rise to topological excitations must give a positive reading for these diagnostics. However, due to spurious contributions [51][52][53][54][55], the generic arguments cannot guarantee that the diagnostics do not give false positives and, moreover, the work gives no interpretation for the magnitude of a positive reading. In our work, we restrict to loop-gas models.…”

Section: Three-dimensional Modelsmentioning

confidence: 99%

Boundary topological entanglement entropy in two and three dimensions

Bridgeman,

Brown,

Elman

2020

Preprint

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The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)-and (3+1)-dimensional loop gas models, both in the bulk and at their boundaries, in terms of the data of their input fusion categories and algebra objects. Central to the formulation of our results are generalized S-matrices. We conjecture a general property of these S-matrices, with proofs provided in many special cases. This includes constructive proofs for categories of ranks 2-5.

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“…For example, the boundary of A 1 ∪ A 0 1 contributes the same nonuniversal terms to S ðnÞ 11 0 and S ðnÞ 11 0 ∪ 33 0 , and these terms have been canceled in I ðnÞ ð11 0 ,33 0 Þ. We note that the locality assumption about nonuniversal terms does not hold in certain systems with the so-called suprious long-range entanglement [39][40][41][42][43][44][45] , which will not be considered in this work. As one test of the universality of I (n) , one can manually add a local bunch of coupled qubits to the state |ψ at an arbitrary location, and observe that the final result of I (n) has no dependence on the state of these qubits.…”

mentioning

confidence: 97%

Anyon quantum dimensions from an arbitrary ground state wave function

Liu

2024

Nat Commun

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Realizing topological orders and topological quantum computation is a central task of modern physics. An important but notoriously hard question in this endeavor is how to diagnose topological orders that lack conventional order parameters. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to detect nontrivial topological order from a ground state wave function, but is far from enough for fully determining the topological order. In this work, we take a key step further in this direction: We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. The choice of the space manifold and the ground state is arbitrary. This protocol is both validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.

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Toy model of boundary states with spurious topological entanglement entropy

Cited by 13 publications

References 24 publications

Subsystem symmetry enriched topological order in three dimensions

Subsystem symmetry enriched topological order in three dimensions

Boundary topological entanglement entropy in two and three dimensions

Anyon quantum dimensions from an arbitrary ground state wave function

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