Topological order in matrix Ising models

Hartnoll, Sean A.; Mazenc, Edward A.; Shi, Zhengyan Darius

doi:10.21468/scipostphys.7.6.081

Cited by 4 publications

(1 citation statement)

References 21 publications

(66 reference statements)

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“…as it is based merely on the appearance of the histograms, not by a quantitative measure. A possible quantitative measure could be given by the method developed in [44]. The application of such measures to our setup is left for future study.…”

Section: Presence Of Two Phasesmentioning

confidence: 99%

Emergence of Lie group symmetric classical spacetimes in canonical tensor model

Kawano,

Sasakura

2021

Preprint

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We analyze a wave function of a tensor model in the canonical formalism, when the argument of the wave function takes Lie group invariant or nearby values. Numerical computations show that there are two phases, which we call the quantum and the classical phases, respectively. In the classical phase, fluctuations are suppressed, and there emerge configurations which are discretizations of the classical geometric spaces invariant under the Lie group symmetries. This is explicitly demonstrated for the emergence of S n (n = 1, 2, 3) for SO(n + 1) symmetries by checking the topological and the geometric (Laplacian) properties of the emerging configurations. The transition between the two phases has the form of splitting/merging of distributions of variables, resembling a matrix model counterpart, namely, the transition between one-cut and two-cut solutions. However this resemblance is obscured by a difference of the mechanism of the distribution in our setup from that in the matrix model. We also discuss this transition as a replica symmetry breaking. We perform various preliminary studies of the properties of the phases and the transition for such values of the argument.

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Section: Presence Of Two Phasesmentioning

confidence: 99%

Emergence of Lie group symmetric classical spacetimes in canonical tensor model

Kawano,

Sasakura

2021

Preprint

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Notes on matrix models (matrix musings)

Anninos¹,

Mühlmann²

2020

J. Stat. Mech.

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In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a matrix-like fashion. We discuss the relation of matrix models to two-dimensional quantum gravity coupled to conformal matter. We provide a brief overview of a variety of more general quantum mechanical matrix models and their putative worldsheet interpretation, as well as other recent developments on large N systems. We end with a discussion of open questions and future directions.

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Emergence of Lie group symmetric classical spacetimes in the canonical tensor model

Kawano

Sasakura

2022

Progress of Theoretical and Experimental Physics

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We analyze a wave function of a tensor model in the canonical formalism, when the argument of the wave function takes Lie group invariant or nearby values. Numerical computations show that there are two phases, which we call the quantum and the classical phases, respectively. In the classical phase, fluctuations are suppressed, and there emerge configurations which are discretizations of the classical geometric spaces invariant under the Lie group symmetries. This is explicitly demonstrated for the emergence of Sn (n = 1, 2, 3) for SO(n + 1) symmetries by checking the topological and the geometric (Laplacian) properties of the emerging configurations. The transition between the two phases has the form of splitting/merging of distributions of variables, resembling a matrix model counterpart, namely, the transition between one-cut and two-cut solutions. However this resemblance is obscured by a difference of the mechanism of the distribution in our setup from that in the matrix model. We also discuss this transition as a replica symmetry breaking. We perform various preliminary studies of the properties of the phases and the transition for such values of the argument.

show abstract

Topological order in matrix Ising models

Cited by 4 publications

References 21 publications

Emergence of Lie group symmetric classical spacetimes in canonical tensor model

Emergence of Lie group symmetric classical spacetimes in canonical tensor model

Notes on matrix models (matrix musings)

Emergence of Lie group symmetric classical spacetimes in the canonical tensor model

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