Topological order, emergent gauge fields, and Fermi surface reconstruction

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Materials Science

Background:

• Topological order describes exotic quantum states characterized by defect expulsion and emergent gauge fields.
• Understanding Fermi surface reconstruction is crucial for explaining metallic behavior, especially in complex materials.
• Symmetry breaking is a traditional paradigm for phase transitions, but alternative mechanisms are sought.

Purpose of the Study:

• To review how topological order and emergent gauge fields reconstruct Fermi surfaces in metals without symmetry breaking.
• To explore the connection between topological order, gauge fields, and metallic states in various models.
• To apply these concepts to understand the pseudogap phase in cuprates.

Main Methods:

• Introduction to topological order using Wegner's quantum gauge theory on a square lattice.
• Analysis of classical XY models at finite temperature and quantum phases of bosons at zero temperature.
• Embedding gauge theories in U(1) gauge theories to study Higgs and confining phases.
• Application to the single-band Hubbard model using SU(2) gauge theory for spin-density-wave fluctuations.

Main Results:

• Identification of metallic states with fluctuating spin-density wave order and topological order.
• Demonstration of emergent, deconfined gauge fields and reconstructed Fermi surfaces with electron-like quasiparticles.
• Absence of broken symmetry in these novel metallic states.
• Relevance of these findings to the pseudogap phase of cuprates.

Conclusions:

• Topological order and emergent gauge fields provide a mechanism for Fermi surface reconstruction without symmetry breaking.
• These findings offer a new perspective on metallic states and their relevance to high-temperature superconductivity.
• The framework is applicable to various condensed matter systems, including bosons and quantum dimer models.