Topological order, emergent gauge fields, and Fermi surface reconstruction.
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| Title: | Topological order, emergent gauge fields, and Fermi surface reconstruction. |
|---|---|
| Authors: | Subir Sachdev1,2,3 sachdev@g.harvard.edu |
| Source: | Reports on Progress in Physics. Jan2019, Vol. 82 Issue 1, p1-1. 1p. |
| Subjects: | Fermi surfaces, Gauge field theory, Symmetry breaking, Metallic surfaces, Quantum field theory, Temperature effect |
| Abstract: | This review describes how topological order associated with the presence of emergent gauge fields can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner’s quantum gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension D = 3; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsion of certain defects, in a state with fluctuating symmetry-breaking order, along with the presence of emergent gauge fields. The phase diagrams of the gauge theory and the XY models are obtained by embedding them in U(1) gauge theories, and by studying their Higgs and confining phases. These ideas are then applied to the single-band Hubbard model on the square lattice. A SU(2) gauge theory describes the fluctuations of spin-density-wave order, and its phase diagram is presented by analogy to the XY models. We obtain a class of zero temperature metallic states with fluctuating spin-density wave order, topological order associated with defect expulsion, deconfined emergent gauge fields, reconstructed Fermi surfaces (with ‘chargon’ or electron-like quasiparticles), but no broken symmetry. We conclude with the application of such metallic states to the pseudogap phase of the cuprates, and note the recent comparison with numerical studies of the Hubbard model and photoemission observations of the electron-doped cuprates. In a detour, we also discuss the influence of Berry phases, and how they can lead to deconfined quantum critical points: this applies to bosons on the square lattice at half-integer filling, and to quantum dimer models. [ABSTRACT FROM AUTHOR] |
| Copyright of Reports on Progress in Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Topological order, emergent gauge fields, and Fermi surface reconstruction. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Subir+Sachdev%22">Subir Sachdev</searchLink><relatesTo>1,2,3</relatesTo><i> sachdev@g.harvard.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Reports+on+Progress+in+Physics%22">Reports on Progress in Physics</searchLink>. Jan2019, Vol. 82 Issue 1, p1-1. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Fermi+surfaces%22">Fermi surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Gauge+field+theory%22">Gauge field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+breaking%22">Symmetry breaking</searchLink><br /><searchLink fieldCode="DE" term="%22Metallic+surfaces%22">Metallic surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+field+theory%22">Quantum field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Temperature+effect%22">Temperature effect</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This review describes how topological order associated with the presence of emergent gauge fields can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner’s quantum gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension D = 3; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsion of certain defects, in a state with fluctuating symmetry-breaking order, along with the presence of emergent gauge fields. The phase diagrams of the gauge theory and the XY models are obtained by embedding them in U(1) gauge theories, and by studying their Higgs and confining phases. These ideas are then applied to the single-band Hubbard model on the square lattice. A SU(2) gauge theory describes the fluctuations of spin-density-wave order, and its phase diagram is presented by analogy to the XY models. We obtain a class of zero temperature metallic states with fluctuating spin-density wave order, topological order associated with defect expulsion, deconfined emergent gauge fields, reconstructed Fermi surfaces (with ‘chargon’ or electron-like quasiparticles), but no broken symmetry. We conclude with the application of such metallic states to the pseudogap phase of the cuprates, and note the recent comparison with numerical studies of the Hubbard model and photoemission observations of the electron-doped cuprates. In a detour, we also discuss the influence of Berry phases, and how they can lead to deconfined quantum critical points: this applies to bosons on the square lattice at half-integer filling, and to quantum dimer models. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Reports on Progress in Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1361-6633/aae110 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: 1 Subjects: – SubjectFull: Fermi surfaces Type: general – SubjectFull: Gauge field theory Type: general – SubjectFull: Symmetry breaking Type: general – SubjectFull: Metallic surfaces Type: general – SubjectFull: Quantum field theory Type: general – SubjectFull: Temperature effect Type: general Titles: – TitleFull: Topological order, emergent gauge fields, and Fermi surface reconstruction. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Subir Sachdev IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 00344885 Numbering: – Type: volume Value: 82 – Type: issue Value: 1 Titles: – TitleFull: Reports on Progress in Physics Type: main |
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