We show that as a result of the axial anomaly, massless fermions at zero temperature define a relativistic quantum superfluid. The anomaly pole implies the existence of a gapless Chiral Density Wave (CDW), i.e. an axion-like acoustic mode of an irrotational and dissipationless Hamiltonian perfect fluid, that is a correlated fermion/anti-fermion pair excitation of the Fermi-Dirac sea. In dimensions the chiral superfluid effective action coincides with that of the Schwinger model as , and the CDW acoustic mode is precisely the Schwinger boson. Since this identity holds also at zero chiral chemical potential, the Dirac vacuum itself may be viewed as a quantum superfluid state. The CDW collective boson is a chiral phase field, which is gapless as a result of a novel, non-linear realization of Goldstone's theorem, extended to this case of symmetry breaking by an anomaly. A new local form of the axial anomaly bosonic effective action in any D even spacetime is given, consistent with superfluidity, and its quantization is shown to be required by the anomalous Schwinger terms in fermion current commutators. In QED$_{4}$ this collective Goldstone mode appears as a massless pole in the axial anomaly triangle diagram, and is responsible for the macroscopic non-dissipative currents of the Chiral Magnetic and Chiral Separation Effects, as well as the Anomalous Hall Effect. In a constant uniform magnetic field an exact dimensional reduction from to occurs and the collective CDW chiral pair excitation propagating along the magnetic field direction is a Chiral Magnetic Wave, which acquires a mass gap . Possible realizations and tests of the theory of collective bosonic excitations due to the anomaly in Dirac/Weyl materials are briefly discussed.
{
"license": [
{
"url": "http://creativecommons.org/licenses/by/3.0/",
"license": "CC-BY-3.0"
}
],
"copyright": [
{
"holder": "The Author(s)",
"statement": "The Author(s)",
"year": "2021"
}
],
"control_number": "60941",
"_oai": {
"updated": "2021-08-25T12:25:38Z",
"id": "oai:repo.scoap3.org:60941",
"sets": [
"NPB"
]
},
"authors": [
{
"affiliations": [
{
"country": "USA",
"value": "Theoretical Division, T-2, MS B283, Los Alamos National Laboratory, Los Alamos, USA"
}
],
"surname": "Mottola",
"email": "emil@lanl.gov",
"full_name": "Mottola, Emil",
"given_names": "Emil"
},
{
"affiliations": [
{
"country": "USA",
"value": "Theoretical Division, T-2, MS B283, Los Alamos National Laboratory, Los Alamos, USA"
},
{
"country": "Russia",
"value": "Institute for Theoretical and Experimental Physics, Moscow, Russia"
}
],
"surname": "Sadofyev",
"email": "sadofyev@itep.ru",
"full_name": "Sadofyev, Andrey V.",
"given_names": "Andrey V."
}
],
"_files": [
{
"checksum": "md5:3fcbb7dba0c732a8c784e5d17751b769",
"filetype": "xml",
"bucket": "c7367b4a-93c8-4d59-8a46-1bad0d091e8d",
"version_id": "1875f7ad-8dff-46ac-9432-6bdde4ddcea2",
"key": "10.1016/j.nuclphysb.2021.115385.xml",
"size": 850215
},
{
"checksum": "md5:369f09bfb9ce22aeb668ed0784b39fd2",
"filetype": "pdf",
"bucket": "c7367b4a-93c8-4d59-8a46-1bad0d091e8d",
"version_id": "cade9a18-5a66-4bad-bd91-2925d00af15f",
"key": "10.1016/j.nuclphysb.2021.115385.pdf",
"size": 679554
},
{
"checksum": "md5:c787e2de4168883ad98aa556d639acec",
"filetype": "pdf/a",
"bucket": "c7367b4a-93c8-4d59-8a46-1bad0d091e8d",
"version_id": "50bfcf67-bae3-462b-9776-17e5bf539723",
"key": "10.1016/j.nuclphysb.2021.115385_a.pdf",
"size": 906861
}
],
"record_creation_date": "2021-03-24T16:30:26.434725",
"titles": [
{
"source": "Elsevier",
"title": "Chiral waves on the Fermi-Dirac sea: Quantum superfluidity and the axial anomaly"
}
],
"collections": [
{
"primary": "Nuclear Physics B"
}
],
"dois": [
{
"value": "10.1016/j.nuclphysb.2021.115385"
}
],
"publication_info": [
{
"journal_volume": "966 C",
"journal_title": "Nuclear Physics B",
"material": "article",
"artid": "115385",
"year": 2021
}
],
"$schema": "http://repo.scoap3.org/schemas/hep.json",
"abstracts": [
{
"source": "Elsevier",
"value": "We show that as a result of the axial anomaly, massless fermions at zero temperature define a relativistic quantum superfluid. The anomaly pole implies the existence of a gapless Chiral Density Wave (CDW), i.e. an axion-like acoustic mode of an irrotational and dissipationless Hamiltonian perfect fluid, that is a correlated fermion/anti-fermion pair excitation of the Fermi-Dirac sea. In <math><mi>D</mi><mo>=</mo><mn>2</mn></math> dimensions the chiral superfluid effective action coincides with that of the Schwinger model as <math><mi>e</mi><mo>\u2192</mo><mn>0</mn></math>, and the CDW acoustic mode is precisely the Schwinger boson. Since this identity holds also at zero chiral chemical potential, the Dirac vacuum itself may be viewed as a quantum superfluid state. The CDW collective boson is a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> chiral phase field, which is gapless as a result of a novel, non-linear realization of Goldstone's theorem, extended to this case of symmetry breaking by an anomaly. A new local form of the axial anomaly bosonic effective action in any D even spacetime is given, consistent with superfluidity, and its quantization is shown to be required by the anomalous Schwinger terms in fermion current commutators. In QED$_{4}$ this collective Goldstone mode appears as a massless pole in the axial anomaly triangle diagram, and is responsible for the macroscopic non-dissipative currents of the Chiral Magnetic and Chiral Separation Effects, as well as the Anomalous Hall Effect. In a constant uniform magnetic field an exact dimensional reduction from <math><mi>D</mi><mo>=</mo><mn>4</mn></math> to <math><mi>D</mi><mo>=</mo><mn>2</mn></math> occurs and the collective <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>\u2212</mo></mrow></msup></math> CDW chiral pair excitation propagating along the magnetic field direction is a Chiral Magnetic Wave, which acquires a mass gap <math><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>B</mi><mo>/</mo><mn>2</mn><msup><mrow><mi>\u03c0</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. Possible realizations and tests of the theory of collective bosonic excitations due to the anomaly in Dirac/Weyl materials are briefly discussed."
}
],
"imprints": [
{
"date": "2021-08-25",
"publisher": "Elsevier"
}
],
"acquisition_source": {
"date": "2021-08-25T09:38:20.314987",
"source": "Elsevier",
"method": "Elsevier",
"submission_number": "0598b3fc058711ecb53772fd3742099d"
}
}