Naoki Yamamoto

Publications (8)7.37 Total impact

• Article: Singular values of the Dirac operator at nonzero density

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
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  ABSTRACT: At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic) condensate. We have constructed low-energy effective theories in different density regimes and derived a number of exact results for the Dirac singular values, including Banks-Casher-type relations for the diquark (or pionic) condensate, Smilga-Stern-type relations for the slope of the singular-value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We also present a rigorous index theorem for non-Hermitian Dirac operators.
  12/2012;
• Article: Banks-Casher-type relation for the BCS gap at high density

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
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  ABSTRACT: We derive a new Banks-Casher-type relation which relates the density of complex Dirac eigenvalues at the origin to the BCS gap of quarks at high density. Our relation is applicable to QCD and QCD-like theories without a sign problem, such as two-color QCD and adjoint QCD with baryon chemical potential, and QCD with isospin chemical potential. It provides us with a method to measure the BCS gap through the Dirac spectrum on the lattice.
  11/2012;
• Source

  Available from: ArXiv

  Article: Singular values of the Dirac operator in dense QCD-like theories

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
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  ABSTRACT: We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.
  10/2011;
• Source

  Available from: ArXiv

  Article: Exact results for two-color QCD at low and high density

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
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  ABSTRACT: We discuss a random matrix theory that was originally constructed to describe two-color QCD at low density in the phase with a nonzero chiral condensate. With a particular choice of a parameter, the same random matrix theory also describes the high-density phase of two-color QCD. In this phase a BCS superfluid of diquark pairs is formed, and the pattern of chiral symmetry breaking is very different from that at low density. Analytical results for the spectral density obtained from this random matrix theory allow for the extraction of the BCS gap from lattice data.
  01/2011;
• Source

  Available from: ArXiv

  Article: Chiral random matrix theory for two-color QCD at high density

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
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  ABSTRACT: We identify a non-Hermitian chiral random matrix theory that corresponds to two-color QCD at high density. We show that the partition function of the random matrix theory coincides with the partition function of the finite-volume effective theory at high density, and that the Leutwyler-Smilga-type spectral sum rules of the random matrix theory are identical to those derived from the effective theory. The microscopic Dirac spectrum of the theory is governed by the BCS gap, rather than the conventional chiral condensate. We also show that with a different choice of a parameter the random matrix theory yields the effective partition function at low density. Comment: 5 pages, no figure; v2. minor changes and text improvements, the version published in Phys. Rev. D
  12/2009;
• Source

  Available from: ArXiv

  Article: Chiral Lagrangian and spectral sum rules for two-color QCD at high density

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
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  ABSTRACT: We report on our analytical study of two-color QCD with an even number of flavors at high baryon density. Based on the pattern of chiral symmetry breaking induced by BCS-type diquark pairing we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We also identify a new epsilon-regime at high baryon density and derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our results can in principle be tested in lattice QCD simulations. Comment: 8 pages, no figure, contribution at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China
  10/2009;
• Source

  Available from: arxiv.org

  Article: Dense QCD in a finite volume.

  Naoki Yamamoto, Takuya Kanazawa
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  ABSTRACT: We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at a finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap Delta. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the Z(2)LxZ(2)R symmetry of the diquark pairing. Our results are universal in the domain Delta(-1)<L<mpi(-1) where L is the linear size of the system and mpi is the pion mass at high density.
  Physical Review Letters 07/2009; 103(3):032001. · 7.37 Impact Factor
• Source

  Available from: ArXiv

  Article: Chiral Lagrangian and spectral sum rules for dense two-color QCD

  Takuya Kanazawa, Tilo Wettig, Naoki Yamamoto
  [show abstract] [hide abstract]
  ABSTRACT: We analytically study two-color QCD with an even number of flavors at high baryon density. This theory is free from the fermion sign problem. Chiral symmetry is broken spontaneously by the diquark condensate. Based on the symmetry breaking pattern we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We identify a new epsilon-regime at high baryon density in which the quark mass dependence of the partition function can be determined exactly. We also derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our results can in principle be tested in lattice QCD simulations. Comment: 24 pages, 1 table, no figure
  06/2009;