Topological order in matrix Ising models

Hartnoll, Sean; Mazenc, Edward; Shi, Zhengyan

doi:10.21468/SciPostPhys.7.6.081

Title: Topological order in matrix Ising models

Abstract

We study a family of models for an N_1 \times N_2 $N_{1} \times N_{2}$ matrix worth of Ising spins S_{aB} $S_{a B}$ . In the large N_i $N_{i}$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single ‘spherical’ constraint. In this way we generalize the results of to a wide class of Ising Hamiltonians with O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) $O (N_{1}, ℤ) \times O (N_{2}, ℤ)$ symmetry. The models can undergo topological large N $N$ phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} $S_{a B}$ becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

Authors:

Hartnoll, Sean ^[1]; Mazenc, Edward ^[1]; Shi, Zhengyan ^[1]

Stanford University

Publication Date:: 2019-12-19

Research Org.:: Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1579979

Alternate Identifier(s):: OSTI ID: 1803258

Grant/Contract Number:: SC0018134

Resource Type:: Published Article

Journal Name:: SciPost Physics Proceedings

Additional Journal Information:: Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 6; Journal ID: ISSN 2542-4653

Publisher:: Stichting SciPost

Country of Publication:: Netherlands

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Topological order in matrix Ising models.  Netherlands: N. p., 2019. 
Web.  doi:10.21468/SciPostPhys.7.6.081.

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                    Hartnoll, Sean, Mazenc, Edward, & Shi, Zhengyan. Topological order in matrix Ising models.  Netherlands.  https://doi.org/10.21468/SciPostPhys.7.6.081

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                    Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Thu .  
"Topological order in matrix Ising models".  Netherlands.  https://doi.org/10.21468/SciPostPhys.7.6.081.

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@article{osti_1579979,

  title        = {Topological order in matrix Ising models},

  author       = {Hartnoll, Sean and Mazenc, Edward and Shi, Zhengyan},

  abstractNote = {We study a family of models for an N_1 \times N_2 N 1 × N 2 matrix worth of Ising spins S_{aB} S a B . In the large N_i N i limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single ‘spherical’ constraint. In this way we generalize the results of to a wide class of Ising Hamiltonians with O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) O ( N 1 , ℤ ) × O ( N 2 , ℤ ) symmetry. The models can undergo topological large N N phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} S a B becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.},

  doi          = {10.21468/SciPostPhys.7.6.081},

  journal      = {SciPost Physics Proceedings},

  number       = 6,

  volume       = 7,

  place        = {Netherlands},

  year         = {2019},

  month        = {12}

}

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Works referenced in this record:

TASI Lectures on Complex Structures
conference, March 2012

Denef, Frederik
Proceedings of the 2010 Theoretical Advanced Study Institute in Elementary Particle Physics, String Theory and Its Applications
DOI: 10.1142/9789814350525_0007