Extracting the Luttinger parameter from a single wave function

Abstract

The low-energy physics of Tomonaga-Luttinger liquids (TLLs) is controlled by the Luttinger parameter. We demonstrate that this parameter can be extracted from a single wave function for one-component TLLs with periodic boundary condition. This method relies on the fact that TLLs are described by conformal field theory in which crosscap states can be constructed. The overlaps between the crosscap states and the ground state as well as some excited states are proved to be universal numbers that directly reveal the Luttinger parameter. In microscopic lattice models, crosscap states are formed by putting each pair of antipodal sites into a maximally entangled state. Analytical and numerical calculations are performed in a few representative models to substantiate the conformal field theory prediction. The extracted Luttinger parameters are generally quite accurate in finite-size systems with moderate lengths, so there is no need to perform data fitting and/or finite-size scaling.

6+10 pages, 2 figures

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Cited by in corpus (6)

• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
• Crosscap states and duality of Ising field theory in two dimensions
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• Exact Quench Dynamics from Thermal Pure Quantum States