Symmetry-protected topological entanglement

Marvian, Iman

doi:10.1103/physrevb.95.045111

Cited by 31 publications

(50 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, while we mainly have studied what is usually referred to as 'long-range entangled' phases, an algebraic approach to symmetry protected phases appears to be reasonable; as a toy model one can consider the Kitaev wire, and divide the system into three parts, as we did in the example of the Fibonacci chain. We conjecture that this can be related to a notion of entanglement entropy for symmetry protected phases, see [58].…”

Section: Summary and Discussionmentioning

confidence: 91%

“…Already in 1989 Longo showed that the quantum dimension d i of a representative of a superselection sector can be obtained as the index of a certain inclusion of von Neumann algebras [32]. Later in 2001 it was shown that for the class of rational conformal field theories on the circle, the total quantum dimension is equal to the index of an inclusion Ì    , very similar to the inclusion Ì   AB AB  [55], and indeed our results are partially motivated by that paper. A similar strategy can be applied to the lattice models that we are interested in.…”

Section: Total Quantum Dimensionmentioning

confidence: 99%

“…holds [11,55], where the sum is over all distinct charges r i , and d i is the corresponding statistical (quantum) dimension. If we do not assume existence of conjugate charges, the index still gives an upper bound on the number of them.…”

Section: Total Quantum Dimensionmentioning

confidence: 99%

“…These are some of the reasons why we prefer to work in an operator-algebraic (or, if one wishes, observable-centric) approach, which does not have these problems. For the benefit of the reader we recall the main definitions and explain how they can be interpreted in the context of quantum mechanics (see also [28,29,59]).…”

Section: Appendix Operator Algebrasmentioning

confidence: 99%

See 3 more Smart Citations

Jones index, secret sharing and total quantum dimension

2017

View full text Add to dashboard Cite

We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. We then argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a 'relative entropy' of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed. 2 [9]. A total quantum dimension that is larger than the number of distinct particles signifies nonabelian anyons [10], since an anyon a is abelian if and only if d a =1. The quantum dimension d a of an anyon of OPEN ACCESS RECEIVED

show abstract

Section: Summary and Discussionmentioning

confidence: 91%

Section: Total Quantum Dimensionmentioning

confidence: 99%

Section: Total Quantum Dimensionmentioning

confidence: 99%

Section: Appendix Operator Algebrasmentioning

confidence: 99%

See 2 more Smart Citations

Jones index, secret sharing and total quantum dimension

2017

View full text Add to dashboard Cite

show abstract

“…We note that the quantity called SPT entanglement, defined in [12] and shown there to label SPT states (at least for abelian groups), is an example of a measurement-based protocol similar to the ones we study.…”

mentioning

confidence: 69%

Disentangling quantum matter with measurements

2020

View full text Add to dashboard Cite

Measurements destroy entanglement. Building on ideas used to study 'quantum disentangled liquids', we explore the use of this effect to characterize states of matter. We focus on systems with multiple components, such as charge and spin in a Hubbard model, or local moments and conduction electrons in a Kondo lattice model. In such systems, measurements of (a subset of) one of the components can leave behind a quantum state of the other that is easy to understand, for example in terms of scaling of entanglement entropy of subregions. We bound the outcome of this protocol, for any choice of measurement, in terms of more standard information-theoretic quantities. We apply this quantum disentangling protocol to several problems of physical interest, including gapless topological phases, heavy fermions, and scar states in Hubbard model. December 20191 arXiv:1912.01027v1 [cond-mat.str-el]

show abstract

String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems

Cheraghi

Tafreshi

Mahdavifar

2019

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

Luttinger liquid (LL) phase refers to a quantum phase which emerges in the ground state phase diagram of quite often low-dimensional quantum magnets as spin-1/2 XX, XYY and frustrated chains. It is believed that the quasi long-range order exists between particles forming the system in the LL phase. Here, at the first step we concentrate on the study of correlated spin particles in the one-dimensional (1D) spin-1/2 XX model which is exactly solvable. We show that the spin-1/2 particles form string orders with an even number of spins in the LL phase of the 1D spin-1/2 XX model. As soon as the transverse magnetic field is applied to the system, string orders with an odd number of spins induce in the LL phase. All ordered strings of spin-1/2 particles will be destroyed at the quantum critical transverse field, hc. No strings exist in the saturated ferromagnetic phase. At the second step we focus on the LL phase in the ground state phase diagram of the 1D spin-1/2 XYY and frustrated ferromagnetic models. We show that the even-string orders exist in the LL phase of the 1D spin-1/2 XYY model but in the LL phase of the 1D spin-1/2 frustrated ferromagnetic model we found all kind of strings. In addition, the existence of a clear relation between the long-distance entanglement and string orders in the LL phase is shown. Also, the effect of the thermal fluctuations on the behavior of the string orders is studied.

show abstract

Symmetry-protected topological entanglement

Cited by 31 publications

References 51 publications

Jones index, secret sharing and total quantum dimension

Jones index, secret sharing and total quantum dimension

Disentangling quantum matter with measurements

String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems

Contact Info

Product

Resources

About