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Topology and Entanglement in Fermion...

Shapourian, Hassan.

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Topology and Entanglement in Fermionic Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topology and Entanglement in Fermionic Systems./
作者:	Shapourian, Hassan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	183 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Contained By:	Dissertations Abstracts International81-03B.
標題:	Condensed matter physics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13863614
ISBN:	9781085614856

Topology and Entanglement in Fermionic Systems.
Shapourian, Hassan.

Topology and Entanglement in Fermionic Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 183 p.

Source: Dissertations Abstracts International, Volume: 81-03, Section: B.

Thesis (Ph.D.)--The University of Chicago, 2019.

This item is not available from ProQuest Dissertations & Theses.

This dissertation brings together ideas from quantum information theory and condensed matter physics to study many-particle systems of fermions. We revisit the structure of the Hilbert space and operator algebras in Fermi systems which provides a natural platform to discuss the notion of entanglement and local operations. We generalize the partial transpose, which is a well-known operation to diagnose entanglement in density matrices of qubits and bosonic systems, to fermionic systems. Our idea was inspired by the observation that time-reversal acts as transposition on density matrices; hence, we looked for a way to apply partial time-reversal to density matrices of fermions.We present a comprehensive set of benchmarks on our proposed definition of fermionic partial transpose and explain the fundamental differences between the bosonic and fermionic partial transpose. We use this new framework and the associated entanglement measure, logarithmic negativity, to study the entanglement content of free fermions with an arbitrary shape of Femi surface in all dimensions as well as topological insulators and superconductors. In particular, we show how thermal fluctuations destroy the quantum coherence of the ground state as temperature is increased.Furthermore, we report the discovery of a surprising connection between topological invariants and the partial transpose in time-reversal symmetric topological insulators and superconductors. In short, we find that partition functions on non-orientable spacetime manifolds such as the Klein bottle or real-projective plane can be obtained by combining untransposed and partially transposed density matrix. This relation turns out to be general and can be used to study various other topological phases protected by anti-unitary symmetries. Similar to the partition functions, the quantities we introduce are complex numbers and their complex phase is a topological invariant. These topological invariants can be regarded as order parameters of topological phases in the sense that they admit discrete values and can only change by jumping from one value to another as we transition from one topological phase to another.

ISBN: 9781085614856Subjects--Topical Terms:

3173567
Condensed matter physics.
Subjects--Index Terms:

Conformal Field Theory

Topology and Entanglement in Fermionic Systems.
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500 $a Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
500 $a Advisor: Ryu, Shinsei.
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506 $a This item is not available from ProQuest Dissertations & Theses.
506 $a This item must not be sold to any third party vendors.
520 $a This dissertation brings together ideas from quantum information theory and condensed matter physics to study many-particle systems of fermions. We revisit the structure of the Hilbert space and operator algebras in Fermi systems which provides a natural platform to discuss the notion of entanglement and local operations. We generalize the partial transpose, which is a well-known operation to diagnose entanglement in density matrices of qubits and bosonic systems, to fermionic systems. Our idea was inspired by the observation that time-reversal acts as transposition on density matrices; hence, we looked for a way to apply partial time-reversal to density matrices of fermions.We present a comprehensive set of benchmarks on our proposed definition of fermionic partial transpose and explain the fundamental differences between the bosonic and fermionic partial transpose. We use this new framework and the associated entanglement measure, logarithmic negativity, to study the entanglement content of free fermions with an arbitrary shape of Femi surface in all dimensions as well as topological insulators and superconductors. In particular, we show how thermal fluctuations destroy the quantum coherence of the ground state as temperature is increased.Furthermore, we report the discovery of a surprising connection between topological invariants and the partial transpose in time-reversal symmetric topological insulators and superconductors. In short, we find that partition functions on non-orientable spacetime manifolds such as the Klein bottle or real-projective plane can be obtained by combining untransposed and partially transposed density matrix. This relation turns out to be general and can be used to study various other topological phases protected by anti-unitary symmetries. Similar to the partition functions, the quantities we introduce are complex numbers and their complex phase is a topological invariant. These topological invariants can be regarded as order parameters of topological phases in the sense that they admit discrete values and can only change by jumping from one value to another as we transition from one topological phase to another.
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653 $a Quantum Field Theory
653 $a Symmetry
653 $a Topological Insulators and Superconductors
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