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Finite-Entanglement Scaling of 2D Metals
Quinten Mortier1, Ming-Hao Li2, Jutho Haegeman1
1Department of Physics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium.
Physical Review Letters
|January 12, 2024
Summary
We extend finite-entanglement scaling to 2D metallic systems, finding entanglement entropy scales with system size and Fermi surface shape. This provides a new method for approximating metallic states using tensor networks.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
Background:
- Finite-entanglement scaling is a powerful tool for understanding quantum many-body systems.
- Previous studies focused on one-dimensional gapless models.
Purpose of the Study:
- To extend finite-entanglement scaling to two-dimensional systems with a Fermi surface.
- To investigate tensor network approximations for metallic states.
Main Methods:
- Analysis of entanglement entropy scaling in two-dimensional systems.
- Utilizing tensor network state approximations.
- Considering the implications of the Lieb-Schultz-Mattis theorem.
Main Results:
- Entanglement entropy scales as S∼Llog[ξf(L/ξ)] in optimal tensor network approximations of metallic states.
- The scaling function f(x) depends on the Fermi surface shape.
- The scaling regime is achievable with numerically tractable bond dimensions.
Conclusions:
- Finite-entanglement scaling provides a viable approach for studying 2D metallic states.
- Tensor network approximations offer a pathway to understanding complex quantum states.
- The Lieb-Schultz-Mattis theorem has implications for these approximations at fractional filling.
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