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We investigate high-frequency optical conductivity near quantum critical points (QCPs), unifying sum rule understanding across dimensions. Interacting Goldstone bosons in superfluid phases significantly alter conductivity and sum rules.

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Area of Science:

  • Condensed matter physics
  • Quantum critical phenomena
  • High-frequency response

Background:

  • Quantum critical points (QCPs) represent unique states of matter where quantum fluctuations drive phase transitions.
  • Understanding the response functions, such as optical conductivity, near QCPs is crucial for characterizing these states.
  • Previous studies often focused on specific dimensions or simplified models, limiting a unified perspective.

Purpose of the Study:

  • To develop a unified understanding of high-frequency response functions, particularly optical conductivity, near QCPs.
  • To investigate the influence of detuning from critical coupling and finite temperature on these response functions.
  • To explore the role of emergent Lorentz invariance and interacting Goldstone bosons.

Main Methods:

  • Analytical calculations using quantum field theory methods, including the large-N O(N) model.
  • Application of gauge-gravity duality to probe response functions.
  • Numerical simulations using quantum Monte Carlo methods on lattice models.

Main Results:

  • A unified framework for understanding sum rules in the vicinity of QCPs across various dimensions and dynamical exponents.
  • Identification of universal coefficients governing high-frequency response in systems with emergent Lorentz invariance.
  • Demonstration that interacting Goldstone bosons in superfluid phases qualitatively modify optical conductivity and sum rules.

Conclusions:

  • The study provides a comprehensive theoretical and numerical framework for high-frequency response near QCPs.
  • The findings highlight the significant impact of emergent symmetries and collective excitations on universal properties.
  • This work offers new insights into the behavior of quantum matter at criticality and in condensed phases.