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Flows of the order parameter of a two-dimensional Fermi system close to the quantum critical point

Version 1.0

Homenda Mateusz; Jakubczyk Paweł; Yamase Hiroyuki, 2025, "Flows of the order parameter of a two-dimensional Fermi system close to the quantum critical point", https://doi.org/10.58132/KG51XY, Dane Badawcze UW, V1

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Description

The research data are related to the article: "Generalized Hertz Action and Quantum Criticality of Two-Dimensional Fermi Systems". These data provide insights into the flow of bosonic parameters near a quantum critical point, forming the basis for the visualizations presented in the publication.

PROJECT

The aim of the project was to establish the low-energy dynamics of a two-dimensional system of fermions coupled to a critical scalar bosonic field. The standard approach, known as Hertz-Millis theory, involves integrating out all fermionic degrees of freedom, which leads to singular vertex bosonic interactions. In this study, we demonstrate how to include a fermionic contribution to bosonic dynamics while avoiding singularities in the bosonic sector. Using the functional renormalization group method, we analyze the flow of bosonic parameters near the quantum critical point, comparing the traditional Hertz-Millis scenario with the new generalized Hertz action.

FILES

The following files contains a numpy array of lists of parameters used for Hertz-Millis and generalized Hertz action calculations respectively:

  • crlistHM.npy
  • crlistGen.npy


The following files contains numpy arrays with numerical data obtained from flow calculations:

  • g 0.0000 l0 0.00 gamma 1.0.npy
  • g 0.0000 l0 1.00 gamma 1.0.npy
  • g 0.0100 l0 0.00 gamma 1.0.npy
  • g 0.0100 l0 1.00 gamma 1.0.npy
  • g 1.0000 l0 0.00 gamma 1.0.npy
  • g 1.0000 l0 1.00 gamma 1.0.npy


For data specification read:

  • readme.txt


METHODOLOGY

The flow were calculated using 'dormand_price' adaptive Runge-Kutta scheme with tolerance up to 10^(-12).

The internal integrals (frequency and momenta) were calculated using Gauss Legendre quadratures. Integration domains were divided into several (up to 10) subdomains with 30-50 nodes each.

The initial condition for quantum critical point was found using bisection-type algorithm.

Subject
Physics
Keyword

quantum phase transition, non-Fermi liquid, renormalization group

Related Publication

Mateusz Homenda, Paweł Jakubczyk, Hiroyuki Yamase, "Generalized Hertz action and quantum criticality of two-dimensional Fermi systems", Phys. Rev. B 110, L121102, DOI: https://doi.org/10.1103/PhysRevB.110.L121102 https://doi.org/10.1103/PhysRevB.110.L121102 doi: 10.1103/PhysRevB.110.L121102

CC0 Creative Commons Zero 1.0 CC0 Creative Commons Zero 1.0

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readme.txt
Plain Text - 2.5 KB - Jan 2, 2025 - 1 Download
MD5: 2c76718197e0d9931f0062c8f91703ce
License: CC0 Creative Commons Zero 1.0
Detailed description of data structure
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crlistHM.npy
Unknown - 256 B - Jan 2, 2025 - 1 Download
MD5: 89710f18bab4ab574b0b798ba1d58446
License: CC0 Creative Commons Zero 1.0
list of initial conditions for Hert-Millis action
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crlistGen.npy
Unknown - 256 B - Jan 2, 2025 - 1 Download
MD5: 4581ff5bcb0f698ba09b93993eeb1063
License: CC0 Creative Commons Zero 1.0
list of initial conditions for generalized Hertz action
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g 0.0000 l0 0.00 gamma 1.0.npy
Unknown - 21.4 MB - Jan 2, 2025 - 1 Download
MD5: 9c7098ffa0a2db28804436492665c0f4
License: CC0 Creative Commons Zero 1.0
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g 0.0000 l0 1.00 gamma 1.0.npy
Unknown - 21.4 MB - Jan 2, 2025 - 1 Download
MD5: 43bacdd4d428a166437184bb07ff6112
License: CC0 Creative Commons Zero 1.0
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g 0.0100 l0 0.00 gamma 1.0.npy
Unknown - 21.4 MB - Jan 2, 2025 - 1 Download
MD5: 2b4b491254bd6d996cb10dee154f1cac
License: CC0 Creative Commons Zero 1.0
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g 0.0100 l0 1.00 gamma 1.0.npy
Unknown - 21.4 MB - Jan 2, 2025 - 1 Download
MD5: 9b2cf3acd09f8e952cf219ce1d1808e9
License: CC0 Creative Commons Zero 1.0
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g 1.0000 l0 0.00 gamma 1.0.npy
Unknown - 21.4 MB - Jan 2, 2025 - 1 Download
MD5: 1e0cef30295af7d4bacbc791fe11f6a5
License: CC0 Creative Commons Zero 1.0
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g 1.0000 l0 1.00 gamma 1.0.npy
Unknown - 21.4 MB - Jan 2, 2025 - 1 Download
MD5: a838ff2789d09599c0dcc055cba2f838
License: CC0 Creative Commons Zero 1.0
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