Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2006-05-29
Phys.Rev.Lett.97:050404,2006
Physics
Condensed Matter
Strongly Correlated Electrons
4 pages, 1 figure, 28 references
Scientific paper
10.1103/PhysRevLett.97.050404
The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have entanglement that 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 the entanglement entropy for a standard class of $z=2$ quantum critical points in two spatial dimensions with scale invariant ground state wave functions: in addition to a nonuniversal ``area law'' contribution proportional to the size of the $AB$ boundary, there is generically a universal logarithmically divergent correction. This logarithmic term is completely determined by the geometry of the partition into subsystems and the central charge of the field theory that describes the equal-time correlations of the critical wavefunction.
Fradkin Eduardo
Moore Joel E.
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