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Topological order, emergent gauge fields, and Fermi surface reconstruction
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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.
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“the discovery of novel topological phases—characterized by topological invariants as opposed to some local order parameter—provides an alternative framework for classifying states of matter79,80.”
From Ultrafast terahertz emission from emerging symmetry-broken materials (2023) · cites this paper as [80]
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Ramazashvili, R. R., Grigoriev, P. D., Helm, T., Kollmannsberger, F., Kunz, M., Biberacher, W., Kampert, E., Fujiwara, H., Erb, A., Wosnitza, J., et al. (2021) · npj Quantum Materials · doi:10.1038/s41535-021-00309-6 · Cited by 14
Hossain, M. S., Mueed, M. A., K., M., Rosales, K. A. V., Chung, Y. J., Pfeiffer, L. N., West, K. W., Baldwin, K. W., & SHAYEGAN, M. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.046601 · Cited by 13
Strange Metals and Black Holes: Insights From the Sachdev-Ye-Kitaev Model
Subir Sachdev, A. (2023) · doi:10.1093/acrefore/9780190871994.013.48 · Cited by 13
On tensor network representations of the (3+1)d toric code
Delcamp, C., & Schuch, N. (2021) · Quantum · doi:10.22331/q-2021-12-16-604 · Cited by 13
Phases and quantum phase transitions in an anisotropic ferromagnetic Kitaev-Heisenberg- Γ magnet
Nanda, A., Dhochak, K., & Bhattacharjee, S. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.235124 · Cited by 12
Anisotropic nonsaturating magnetoresistance observed in HoMn6Ge6 : A kagome Dirac semimetal
Low, A., Bhowmik, T. K., Ghosh, S. K., & Thirupathaiah, S. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.195104 · Cited by 11
Deep learning lattice gauge theories
Apte, A., Córdova, C., Huang, T.-C., & Ashmore, A. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.165133 · Cited by 18
The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
Subir Sachdev, A. (2025) · Physica C Superconductivity · doi:10.1016/j.physc.2025.1354707 · Cited by 11
Three-dimensional Abelian and non-Abelian gauge Higgs theories
Bonati, C., Andrea Pelissetto, C., & Vicari, E. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.05.004 · Cited by 17
Metadata
- Authors
- Sachdev, S.
- ORCID
- Sachdev, Subir
- Venue
- Reports on Progress in Physics
- Publisher
- IOP Publishing
- Published
- 2018-11-07
- Volume
- 82
- Issue
- 1
- Pages
- 014001
- ISSN
- 0034-4885 (ISSN-L)
- 1361-6633
- OpenAlex
- W2888540086
- Cited by
- 227
- References
- 110
- Citations by year
- 2026: 16 · 2025: 34 · 2024: 28 · 2023: 28 · 2022: 25 · 2021: 39 · 2020: 42 · 2019: 15
- FWCI
- 12.97
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Reports on Progress in Physics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- topological order, emergent gauge fields, Fermi surface reconstruction, square lattice, XY model, Higgs phase, confining phase, single-band Hubbard model, spin density wave, deconfined quantum critical point, Berry phase, quantum dimer model, pseudogap phase, cuprate superconductors, electron-doped cuprates, quasiparticles
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