TY - JOUR

T1 - Entanglement entropy of 2D conformal quantum critical points

T2 - Hearing the shape of a quantum drum

AU - Fradkin, Eduardo

AU - Moore, Joel E.

PY - 2006

Y1 - 2006

N2 - The entanglement entropy of a pure quantum state of a bipartite system A∪B is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

AB - The entanglement entropy of a pure quantum state of a bipartite system A∪B is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

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U2 - 10.1103/PhysRevLett.97.050404

DO - 10.1103/PhysRevLett.97.050404

M3 - Article

AN - SCOPUS:33746922351

VL - 97

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 5

M1 - 050404

ER -