Beyond Li-Haldane Counting: A Close Look at Chiral Topological Order in the Entanglement Spectra of (2+1)-Dimensional Spin Liquid Ground States, with a Focus on PEPS- [electronic resource]
Beyond Li-Haldane Counting: A Close Look at Chiral Topological Order in the Entanglement Spectra of (2+1)-Dimensional Spin Liquid Ground States, with a Focus on PEPS- [electronic resource]
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214101235
- ISBN
- 9798380158466
- DDC
- 530
- 서명/저자
- Beyond Li-Haldane Counting: A Close Look at Chiral Topological Order in the Entanglement Spectra of (2+1)-Dimensional Spin Liquid Ground States, with a Focus on PEPS - [electronic resource]
- 발행사항
- [S.l.]: : University of California, Santa Barbara., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(202 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
- 주기사항
- Advisor: Ludwig, Andreas W. W.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Santa Barbara, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 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.
- 일반주제명
- Quantum physics.
- 일반주제명
- Statistical physics.
- 기타저자
- University of California, Santa Barbara Physics
- 기본자료저록
- Dissertations Abstracts International. 85-02B.
- 기본자료저록
- Dissertation Abstract International
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