Topological order, emergent gauge fields, and Fermi surface reconstruction

Abstract

We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ 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 $Z_2$ 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.

56 pages, 25 figures. Review article, comments welcome. Partly based on lectures at the 34th Jerusalem Winter School in Theoretical Physics: New Horizons in Quantum Matter, December 27, 2016 - January 5, 2017, https://tinyurl.com/y8oglg4e ;(v2,v3,v4,v5) added refs, figures, remarks

References in corpus (29)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Fractionalized Fermi liquids
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• On the stability of U(1) spin liquids in two dimensions
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Putting competing orders in their place near the Mott transition
• Planes, Chains, and Orbits: Quantum Oscillations and High Magnetic Field Heat Capacity in Underdoped YBCO
• Algebraic charge liquids
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Quantum Oscillations in Hole-Doped Cuprates
• Topological order in the pseudogap metal
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Fluctuating spin density waves in metals
• Fermi surfaces and gauge-gravity duality
• Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• Sum Rules and Ward Identities in the Kondo Lattice
• Destruction of Neel order in the cuprates by electron-doping
• Fermi surface reconstruction in hole-doped t-J models without long-range antiferromagnetic order
• Higgs criticality in a two-dimensional metal
• Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes
• Majorana liquids: the complete fractionalization of the electron
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Exact solution of a two-species quantum dimer model for pseudogap metals
• Electron spectral functions in a quantum dimer model for topological metals

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