Abstract
A classical analogue of the entanglement entropy is calculated on the system boundary of the two-dimensional Edwards-Anderson model, where the nearest-neighbor interaction is stochastically chosen from +J and -J. The boundary spin distribution is obtained by means of the time-evolving block decimation (TEBD) method, where the random ensemble is created from the successive multiplications of position-dependent transfer matrices, whose width is up to N = 300. The random average of the entanglement entropy is calculated on the Nishimori line, and it is confirmed that the entanglement entropy shows critical singularity at the Nishimori point. The central charge of the boundary state is estimated.
Highlights
The effect of randomness on magnetic phenomena has been one of the issues in statistical physics
The entanglement entropy S is calculated on the system boundary of the square-lattice ±J Ising model by the timeevolving block decimation (TEBD) method
The partial sum V in Eq (8) can be obtained with high numerical precision by the TEBD method,13–15) where V is represented in the form of the canonical matrix product.27–29)
Summary
It is confirmed that 〈S〉 shows critical singularity around the Nishimori point
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