TY - JOUR

T1 - Capacity of entanglement and the distribution of density matrix eigenvalues in gapless systems

AU - Nakagawa, Yuya O.

AU - Furukawa, Shunsuke

N1 - Funding Information:
Y.O.N. thanks Y. Nakaguchi and T. Numasawa for valuable discussions. The authors thank Z. Papic for useful correspondence. The authors would like to thank the Yukawa Institute for Theoretical Physics at Kyoto University for hospitality during the long-term workshop YITP-T-16-01 “Quantum Information in String Theory and Many-body Systems” (May 2016), where part of our work was done. Y.O.N. was supported by the Advanced Leading Graduate Course for Photon Science (ALPS) of the Japan Society for the Promotion of Science (JSPS) and by JSPS KAKENHI Grant No. JP16J01135. S.F. was supported by JSPS KAKENHI Grant No. JP25800225 and the Matsuo Foundation.

PY - 2017/11/7

Y1 - 2017/11/7

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.96.205108

DO - 10.1103/PhysRevB.96.205108

M3 - Article

AN - SCOPUS:85039041192

VL - 96

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 2469-9950

IS - 20

M1 - 205108

ER -