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Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Symmetry-Enforced Fermi Surfaces.

Minho Luke Kim1, Salvatore D Pace1, Shu-Heng Shao2

  • 1Massachusetts Institute of Technology, Department of Physics, Cambridge 02139, USA.

Physical Review Letters
|May 15, 2026
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Researchers discovered a new symmetry in quantum lattice fermion models that guarantees a Fermi surface, a key feature for gapless states. This symmetry, combining U(1) fermion number and Majorana translation, reveals fundamental properties of quantum matter.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Materials Science

Background:

  • Symmetry principles are crucial in understanding quantum phenomena.
  • The existence of Fermi surfaces is a hallmark of many conducting materials.
  • Gaplessness in quantum systems often arises from specific symmetries.

Purpose of the Study:

  • To identify a novel symmetry that enforces the presence of a Fermi surface in quantum lattice fermion models.
  • To explore the implications of this symmetry for gapless states in condensed matter.
  • To characterize the resulting symmetry group and its properties.

Main Methods:

  • Constructing a new symmetry group from on-site U(1) fermion number symmetry and non-on-site Majorana translation symmetry.
  • Analyzing quantum lattice fermion models on d-dimensional Bravais lattices.
  • Investigating the relationship between the constructed symmetry group and existing concepts like ersatz Fermi liquids.

Main Results:

  • A novel symmetry is identified that universally enforces a Fermi surface in symmetric quantum lattice fermion models.
  • These symmetry-enforced Fermi surfaces represent a robust form of symmetry-enforced gaplessness.
  • The symmetry group is identified as a noncompact Lie group related to the Onsager algebra.
  • The UV symmetry group contains a specific subgroup of the ersatz Fermi liquid U(1) symmetry.
  • Symmetry-enforced Fermi surfaces generically exhibit at least two noncontractible components.

Conclusions:

  • The discovered symmetry provides a fundamental mechanism for gaplessness in quantum materials.
  • This work deepens the understanding of the interplay between symmetry, topology, and electronic properties in condensed matter.
  • The findings have implications for the design and characterization of novel quantum materials.