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Grupo de renormalización para la localización de Anderson en redes de alta dimensión

Boris L Altshuler1, Vladimir E Kravtsov2, Antonello Scardicchio2,3

  • 1Physics Department, Columbia University, New York, NY 10027.

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Resumen

Este estudio explora las propiedades críticas del modelo de Anderson utilizando métodos de grupo de renormalización. Revela cómo las dimensiones fractales evolucionan con la dimensionalidad, uniendo diferentes marcos teóricos para las transiciones de Anderson.

Palabras clave:
Localización de Andersonlocalización de muchos cuerposGrupo de renormalización

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Área de la Ciencia:

  • Física de la materia condensada
  • Mecánica estadística
  • Sistemas Cuánticos

Sus antecedentes:

  • El modelo de Anderson describe la localización de electrones en sistemas desordenados.
  • Comprender las propiedades críticas y las transiciones es crucial para la física de la materia condensada.
  • El trabajo anterior introdujo un nuevo marco de grupo de renormalización (RG) para las transiciones de Anderson.

Objetivo del estudio:

  • Para investigar la dependencia dimensional de las propiedades críticas en el modelo de Anderson.
  • Para analizar el comportamiento de la función beta para la dimensión fractal.
  • Para conciliar diferentes expansiones teóricas y comprender el papel de los exponentes irrelevantes.

Principales métodos:

  • Utilizando un marco de grupo de renormalización (GR) recientemente introducido.
  • Analizando la función beta para la dimensión fractal en varios límites dimensionales.
  • Empleando expansiones alrededor de los resultados de gráficos regulares aleatorios (RRG).
  • Investigando el surgimiento de exponentes irrelevantes de modelos sigma no lineales.

Principales resultados:

  • Demostró una evolución suave de la función beta de la dimensión fractal desde las dimensiones d hasta los límites RRG.
  • Se ha mostrado cómo se pueden conciliar las expansiones d-dimensional y RRG.
  • Ilustró la dependencia de dimensionalidad de la trayectoria del grupo de renormalización gobernada por el exponente irrelevante.
  • Propuso una conjetura para un límite inferior en la dimensión fractal.

Conclusiones:

  • El marco RG desarrollado proporciona un enfoque unificado para estudiar las transiciones de Anderson a través de diferentes dimensiones.
  • Los hallazgos ofrecen información sobre el comportamiento de los sistemas cuánticos desordenados.
  • Este trabajo sienta las bases para futuras investigaciones sobre sistemas cuánticos de muchos cuerpos y no equilibrio.