자료유형  

 학위논문

Control Number  

0016933348

International Standard Book Number  

9798380158466

Dewey Decimal Classification Number  

530

Main Entry-Personal Name  

Arildsen, Mark Jesse.

Publication, Distribution, etc. (Imprint  

[S.l.] : University of California, Santa Barbara., 2023

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2023

Physical Description  

1 online resource(202 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 85-02, Section: B.

General Note  

Advisor: Ludwig, Andreas W. W.

Dissertation Note  

Thesis (Ph.D.)--University of California, Santa Barbara, 2023.

Restrictions on Access Note  

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

Summary, Etc.  

요약The entanglement spectrum (ES) has been a successful tool for the exploration of (2+1)-dimensional chiral topological states, through Li and Haldane's method of counting degeneracies in the low-lying ES characteristic of an underlying conformal field theory (CFT). We develop an quantitative understanding of the splitting of these degeneracies in the real space ES, at fixed momentum, that occurs at finite size, based on a Generalized Gibbs Ensemble (GGE) of local conservation laws that arise directly from, and are thus controlled by, the chiral CFT. These conservation laws come from viewing the conformal boundary state description of the ES as a quantum quench. We apply this by computing such conservation laws for chiral SU(2)-level-one and -level-two, and later chiral SU(3)-level-one, Wess-Zumino-Witten CFTs, and successfully matching these with numerically calculated entanglement spectra for corresponding chiral spin liquid states, including PEPS.For the chiral SU(2)-level-two case, we find that essential to the GGE are local integrals of operators of fractional dimension, as proposed by Cardy in Ref. [2]. One such operator, G(x), has lower conformal dimension than the energy-momentum tensor, T(x), and we discuss possible consequences of this. Meanwhile in the chiral SU(3)-level-one case, we find that integrals of odd-dimensional operators are available from the CFT, which are the only ones that can be responsible for breaking the degeneracy of SU(3) conjugates, but they are excluded from the GGE by discrete symmetries, for a chiral state. This prediction of conjugate degeneracy in the chiral SU(3)-level-one spin liquid state is backed by the numerical ES to which we match our chiral SU(3)-level-one ensemble of conservation laws.Along the way, we develop a "doubled" SU(3)-level-one theory to fully explain the low-lying entanglement spectrum of an SU(3) spin liquid PEPS that strongly breaks time-reversal symmetry and possesses chiral SU(3)-level-one Li-Haldane counting in some ES sectors, but not others. This clarifies the non-chirality of that state. We then use the PEPS's sectors which exhibit Li-Haldane state counting of a chiral state, but which do exhibit breaking of the degeneracy of SU(3) conjugates, to exhibit a clear contrast with the chiral SU(3)-level-one spin liquid state we previously examined, and demonstrate the utility of broken conjugate degeneracy as a diagnostic of the absence of chirality.

Subject Added Entry-Topical Term  

Condensed matter physics.

Subject Added Entry-Topical Term  

Quantum physics.

Subject Added Entry-Topical Term  

Statistical physics.

Index Term-Uncontrolled  

Conformal field theory

Index Term-Uncontrolled  

Projected Entangled Pair States

Index Term-Uncontrolled  

Quantum entanglement

Index Term-Uncontrolled  

Quantum spin liquid

Index Term-Uncontrolled  

Quantum statistical mechanics

Index Term-Uncontrolled  

Topological order

Added Entry-Corporate Name  

University of California, Santa Barbara Physics

Host Item Entry  

Dissertations Abstracts International. 85-02B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:639685