Capacity of entanglement and the distribution of density matrix eigenvalues in gapless systems

Yuya O. Nakagawa, Shunsuke Furukawa

研究成果: Article査読

8 被引用数 (Scopus)


We propose that the properties of the capacity of entanglement (COE) in gapless systems can efficiently be investigated through the use of the distribution of eigenvalues of the reduced density matrix (RDM). The COE is defined as the fictitious heat capacity calculated from the entanglement spectrum. Its dependence on the fictitious temperature can reflect the low-temperature behavior of the physical heat capacity and thus provide a useful probe of gapless bulk or edge excitations of the system. Assuming a power-law scaling of the COE with an exponent α at low fictitious temperatures, we derive an analytical formula for the distribution function of the RDM eigenvalues. We numerically test the effectiveness of the formula in a relativistic free scalar boson in two spatial dimensions and find that the distribution function can detect the expected α=3 scaling of the COE much more efficiently than the raw data of the COE. We also calculate the distribution function in the ground state of the half-filled Landau level with short-range interactions and find better agreement with the α=2/3 formula than with the α=1 one, which indicates a non-Fermi-liquid nature of the system.

ジャーナルPhysical Review B
出版ステータスPublished - 2017 11月 7

ASJC Scopus subject areas

  • 電子材料、光学材料、および磁性材料
  • 凝縮系物理学


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