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Entanglement scaling in critical two-dimensional fermionic and bosonic systems

2006; American Physical Society; Volume: 74; Issue: 2 Linguagem: Inglês

10.1103/physreva.74.022329

1538-4446

Thomas Barthel, Ming-Chiang Chung, Ulrich Schollwöck,

Advanced Thermodynamics and Statistical Mechanics

We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way and calculate the scaling of the entanglement entropy of finite systems in an infinite universe exactly. For critical fermionic two-dimensional (2D) systems at $T=0$, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, then we find an area law with a sublogarithmic correction. For a critical bosonic 2D array of coupled oscillators at $T=0$, our results show that the entanglement entropy follows the area law without corrections.