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Extracting the Luttinger Parameter from a Single Wave Function.

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A new method extracts the Luttinger parameter, crucial for Tomonaga-Luttinger liquids (TLLs), from a single wavefunction. This approach simplifies analyzing TLLs by utilizing crosscap states derived from conformal field theory.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Many-Body Physics

Background:

  • Tomonaga-Luttinger liquids (TLLs) are fundamental 1D quantum systems.
  • Low-energy physics in TLLs is governed by the Luttinger parameter.
  • Extracting the Luttinger parameter is essential for understanding TLL properties.

Purpose of the Study:

  • To develop a novel method for extracting the Luttinger parameter in one-component TLLs.
  • To demonstrate the utility of conformal field theory and crosscap states for parameter extraction.
  • To provide an accurate and efficient technique applicable to both analytical and numerical studies.

Main Methods:

  • Utilizing conformal field theory to construct crosscap states for TLLs.
  • Calculating overlaps between crosscap states and ground/excited states of the TLL.
  • Implementing the method in microscopic lattice models with periodic boundary conditions.

Main Results:

  • The Luttinger parameter can be directly extracted from overlaps with universal numbers.
  • Crosscap states are formed by maximally entangling antipodal sites in lattice models.
  • Analytical and numerical calculations confirm the accuracy of the method in finite-size systems.

Conclusions:

  • The proposed method offers a direct and accurate way to determine the Luttinger parameter.
  • This technique bypasses the need for complex data fitting and finite-size scaling.
  • The findings provide a valuable tool for the study of one-dimensional quantum systems.