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Persistent homology analysis for dense QCD effective model with heavy quarks
High Energy Physics - Lattice · Submitted 22 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition.
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The abstract, sentence by sentence
The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it as QCD-like Potts model. The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. | contribution 0.56 | 0.92 | 0.04 | asserted 0.92 |
| s2 | We call it as QCD-like Potts model. | contribution 0.57 | 0.62 | 0.03 | asserted 0.98 |
| s3 | The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. | background 0.52 | 0.12 | 0.04 | hedged possibility 0.91 |
| s4 | Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. | method 0.95 | 0.94 | 0.05 | asserted 0.97 |
| s5 | We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition. | result 0.98 | 0.94 | 0.78 | asserted 1.00 |
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The paper
Original abstract
The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it as QCD-like Potts model. The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition.
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How the literature uses it
8 arXiv papers cite this in 8 sentences
Papers citing it · 6 sentences without a confident label
Cites it as background 2 papers
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In order to provide their usefulness to examine phase transitions, many techniques, such as principal component analysis (PCA) [ref] , t-SNE [ref] , convolutional neural networks [ref] , restricted Boltzmann machines [ref] , intrinsic dimension analysis [ref] , and persistence homology [ref] , have been used to identify the critical points in effective (spin and/or fermionic) models.
Learning quantum phase transitions through Topological Data Analysis · Introduction · 0.81
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In the related context of phase transitions, persistent homology allowed for insights into critical phenomena and phase structures [ref] .
Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis · Introduction · 0.94
What it cites · 20 sentences without a confident label
Builds on 1 paper
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To make the Potts model relate to QCD, we here consider following extension of the Potts energy based on Ref. [ref] ; [equation] where $N_f$ denotes the number of flavor where we assume all favors are degenerated, $h_±$ is the external field explained in Eq. ([ref]) and $Φ_x$ ($Φ̅_x$) does the $ℤ_3$ values (its conjugate) on each site shown in Eq. ([ref]); it corresponds to the Polyakov-loop in QCD where the number of color is set to $3$.
Solution of the Complex Action Problem in the Potts Model for Dense QCD · Map of chemical potential to external field · 0.81
Uses the method or tool of 1 paper
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To simply visualize the persistent diagram, the averaged ratio of the birth and death times has been proposed in Ref. [ref] ; [equation] where $N_h$ is number of all possible holes and $∑_i$ means that we sum up $t_D/t_B$ for all possible holes.
Persistent homology analysis of deconfinement transition in effective Polyakov-line model · Ratio of birth and death times · 0.89
Cites as support 1 paper
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The important point is that it is known that the $μ_R$ region and the $μ_iso$ region are equivalent in the region where the pion condensation does not appear at least in the large $N_c$ limit; see Ref. [ref] as an example.
Universality of Phases in QCD and QCD-like Theories · Introduction · 0.96
Cites as background 12 papers
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In this paper, we employ the three-dimensional three-state Potts model with the external field as the QCD effective model with heavy quarks; see Refs. [ref] for details of the relation between the Potts model and QCD.
Solution of the Complex Action Problem in the Potts Model for Dense QCD · Formalism · 0.80
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In this paper, we employ the three-dimensional three-state Potts model with the external field as the QCD effective model with heavy quarks; see Refs. [ref] for details of the relation between the Potts model and QCD.
Information theoretical view of QCD effective model with heavy quarks · Formalism · 0.80
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In this paper, we employ the three-dimensional three-state Potts model with the external field as the QCD effective model with heavy quarks; see Refs. [ref] for details of the relation between the Potts model and QCD.
The 3-state Potts model as a heavy quark finite density laboratory · Formalism · 0.80
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