The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry
For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of <i>u</i> and <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>d</mi>...
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MDPI AG
2020-02-01
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| Online Access: | https://www.mdpi.com/2571-712X/3/1/7 |
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| author | Bastian B. Brandt Francesca Cuteri Gergely Endrodi Sebastian Schmalzbauer |
| author_facet | Bastian B. Brandt Francesca Cuteri Gergely Endrodi Sebastian Schmalzbauer |
| author_sort | Bastian B. Brandt |
| collection | DOAJ |
| description | For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of <i>u</i> and <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>d</mi> <mo>¯</mo> </mover> </semantics> </math> </inline-formula> Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mi>I</mi> </msub> <mo>≥</mo> <msub> <mi>m</mi> <mi>π</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential). |
| first_indexed | 2024-04-13T09:29:30Z |
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| language | English |
| last_indexed | 2024-04-13T09:29:30Z |
| publishDate | 2020-02-01 |
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| series | Particles |
| spelling | doaj.art-ef3ffc161b354ed8be9049eecfbbcf312022-12-22T02:52:19ZengMDPI AGParticles2571-712X2020-02-0131808610.3390/particles3010007particles3010007The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetryBastian B. Brandt0Francesca Cuteri1Gergely Endrodi2Sebastian Schmalzbauer3Institute for Theoretical Physics, Goethe University, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, GermanyInstitute for Theoretical Physics, Goethe University, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, GermanyInstitute for Theoretical Physics, Goethe University, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, GermanyInstitute for Theoretical Physics, Goethe University, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, GermanyFor large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of <i>u</i> and <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>d</mi> <mo>¯</mo> </mover> </semantics> </math> </inline-formula> Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mi>I</mi> </msub> <mo>≥</mo> <msub> <mi>m</mi> <mi>π</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).https://www.mdpi.com/2571-712X/3/1/7lattice qcdisospinbcs phase |
| spellingShingle | Bastian B. Brandt Francesca Cuteri Gergely Endrodi Sebastian Schmalzbauer The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry Particles lattice qcd isospin bcs phase |
| title | The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry |
| title_full | The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry |
| title_fullStr | The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry |
| title_full_unstemmed | The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry |
| title_short | The Dirac spectrum and the BEC-BCS crossover in QCD at nonzero isospin asymmetry |
| title_sort | dirac spectrum and the bec bcs crossover in qcd at nonzero isospin asymmetry |
| topic | lattice qcd isospin bcs phase |
| url | https://www.mdpi.com/2571-712X/3/1/7 |
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