Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
arXiv:2005.07924 · doi:10.1103/PhysRevE.104.044137
Abstract
We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum -state Potts model and transverse field spin- XY model are considered numerically by using the infinite matrix product state (iMPS) approach. As a system parameter varies, block-block mutual informations exhibit a singular behavior that enables to identify critical points for quantum phase transition. As happens with the von Neumann entanglement entropy of a single block, at the critical points, the block-block mutual information between the two lattice-blocks of contiguous sites equally partitioned in a lattice-block of contiguous sites shows a logarithmic leading behavior, which yields the central charge of the underlying conformal field theory. As the separation between the two lattice-blocks increases, the mutual information reveals a consistent power-law decaying behavior for various truncation dimensions and lattice-block sizes. The critical exponent of block-block mutual information in the thermodynamic limit is estimated by extrapolating the exponents of power-law decaying regions for finite truncation dimensions. For a given lattice-block size , the critical exponents for the same universality classes seem to have very close values each other. Whereas the critical exponents have different values to a degree of distinction for different universality classes. As the lattice-block size becomes bigger, the critical exponent becomes smaller.
arXiv comment11 pages, 11 figures
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