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Quantum Entanglement and Quantum Cha...

Tan, Mao Tian.

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Quantum Entanglement and Quantum Chaos in Field Theory and Many-Body Physics.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quantum Entanglement and Quantum Chaos in Field Theory and Many-Body Physics./
作者:	Tan, Mao Tian.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	276 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
Contained By:	Dissertations Abstracts International83-01B.
標題:	Physics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28414466
ISBN:	9798516958991

Quantum Entanglement and Quantum Chaos in Field Theory and Many-Body Physics.
Tan, Mao Tian.

Quantum Entanglement and Quantum Chaos in Field Theory and Many-Body Physics. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 276 p.

Source: Dissertations Abstracts International, Volume: 83-01, Section: B.

Thesis (Ph.D.)--The University of Chicago, 2021.

This item must not be sold to any third party vendors.

The thesis begins with an analysis of the operator entanglement of the unitary time evolution operator. Three different conformal field theories are examined: the free Dirac fermion, the compactified boson for varying radii and the holographic conformal field theories. The first two conformal field theories are examples of integrable conformal field theories while the last one is the prime example of a chaotic field theory. The key quantity studied is the late-time saturation value of the tripartite operator mutual information (TOMI) as it directly quantifies the amount of information scrambled by the time evolution operator. The more negative this quantity, the greater the degree of information delocalization. Furthermore, a lower bound on the late-time TOMI is proposed. The free fermion CFT is found to have vanishing TOMI, indicating a complete lack of information scrambling. On the other extreme, the holographic conformal field theory is found to have a maximally negative late-time TOMI, saturating the proposed lower bound. This is consistent with the currently held belief that holographic systems are maximally chaotic. The compactified bosons have a late-time TOMI that is non-vanishing and yet far from the lower bound, indicating some intermediate amount of information scrambling. Besides quantum field theories, the unitary operator entanglement in disordered condensed matter systems is also analyzed. The Anderson insulator, which is a system of disordered free fermions, has a vanishing TOMI, which is unsurprising. The most fascinating behavior is that of a many-body localized phase. It is widely known that systems in these phases are non-thermalizing and non-chaotic, and yet their late-time TOMI is found to scale like a volume law, albeit with an exponentially long saturation time. This implies that many-body localized systems can scramble information. This example shows that there is a distinction between quantum chaos and information scrambling, and that the final definition of quantum chaos must consider the time scale involved. The operator negativity is studied in the third chapter. It is another measure of entanglement that only captures quantum correlations unlike the mutual information which captures both classical and quantum correlations. The conclusions drawn from the operator negativity are the same as those of the operator mutual information. The operator entanglement of a local operator is also considered. The local operator entanglement has a straightforward interpretation in terms of the butterfly effect and thus provides a direct probe of quantum chaos. The late-time TOMI for the single site parity operator in a free fermion chain and the Hadamard and CNOT gates in Clifford circuits, which are examples of non-chaotic systems, have a negative value of at most order one, while the late-time TOMI of a local operator in the holographic CFTs or the random unitary circuits are maximally negative. This demonstrates the ability of local operator entanglement in distinguishing between chaotic and non-chaotic systems. The final chapter is about the Renyi and symmetry-resolved entanglement entropy of a two-dimensional Fermi gas which are calculated using multi-dimensional bosonization. When the Fermi momentum is large, the symmetry-resolved entanglement exhibits the equipartition of entanglement.

ISBN: 9798516958991Subjects--Topical Terms:

516296
Physics.
Subjects--Index Terms:

Quantum chaos

Quantum Entanglement and Quantum Chaos in Field Theory and Many-Body Physics.
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500 $a Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
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506 $a This item must not be sold to any third party vendors.
520 $a The thesis begins with an analysis of the operator entanglement of the unitary time evolution operator. Three different conformal field theories are examined: the free Dirac fermion, the compactified boson for varying radii and the holographic conformal field theories. The first two conformal field theories are examples of integrable conformal field theories while the last one is the prime example of a chaotic field theory. The key quantity studied is the late-time saturation value of the tripartite operator mutual information (TOMI) as it directly quantifies the amount of information scrambled by the time evolution operator. The more negative this quantity, the greater the degree of information delocalization. Furthermore, a lower bound on the late-time TOMI is proposed. The free fermion CFT is found to have vanishing TOMI, indicating a complete lack of information scrambling. On the other extreme, the holographic conformal field theory is found to have a maximally negative late-time TOMI, saturating the proposed lower bound. This is consistent with the currently held belief that holographic systems are maximally chaotic. The compactified bosons have a late-time TOMI that is non-vanishing and yet far from the lower bound, indicating some intermediate amount of information scrambling. Besides quantum field theories, the unitary operator entanglement in disordered condensed matter systems is also analyzed. The Anderson insulator, which is a system of disordered free fermions, has a vanishing TOMI, which is unsurprising. The most fascinating behavior is that of a many-body localized phase. It is widely known that systems in these phases are non-thermalizing and non-chaotic, and yet their late-time TOMI is found to scale like a volume law, albeit with an exponentially long saturation time. This implies that many-body localized systems can scramble information. This example shows that there is a distinction between quantum chaos and information scrambling, and that the final definition of quantum chaos must consider the time scale involved. The operator negativity is studied in the third chapter. It is another measure of entanglement that only captures quantum correlations unlike the mutual information which captures both classical and quantum correlations. The conclusions drawn from the operator negativity are the same as those of the operator mutual information. The operator entanglement of a local operator is also considered. The local operator entanglement has a straightforward interpretation in terms of the butterfly effect and thus provides a direct probe of quantum chaos. The late-time TOMI for the single site parity operator in a free fermion chain and the Hadamard and CNOT gates in Clifford circuits, which are examples of non-chaotic systems, have a negative value of at most order one, while the late-time TOMI of a local operator in the holographic CFTs or the random unitary circuits are maximally negative. This demonstrates the ability of local operator entanglement in distinguishing between chaotic and non-chaotic systems. The final chapter is about the Renyi and symmetry-resolved entanglement entropy of a two-dimensional Fermi gas which are calculated using multi-dimensional bosonization. When the Fermi momentum is large, the symmetry-resolved entanglement exhibits the equipartition of entanglement.
590 $a School code: 0330.
650 4 $a Physics. $3 516296
650 4 $a Quantum physics. $3 726746
650 4 $a Theoretical physics. $3 2144760
650 4 $a Circuits. $3 3555093
650 4 $a Approximation. $3 3560410
650 4 $a Lattice theory. $3 532024
650 4 $a Codes. $3 3560019
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650 4 $a Hilbert space. $3 558371
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653 $a Field theory
653 $a Many-body physics
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792 $a 2021
793 $a English
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