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Formation probabilities in quantum critical chains and Casimir effect
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abstract
We find a connection between logarithmic formation probabilities of two disjoint intervals of quantum critical spin chains and the Casimir energy of two aligned needles in two dimensional classical critical systems. Using this connection we provide a formula for the logarithmic formation probability of two disjoint intervals in generic $1+1$ dimensional critical systems. The quantity is depenedent on the full structure of the underlying conformal field theory and so useful to find the universality class of the critical system. The connection that we find also provides a very efficient numerical method to calculate the Casimir energy between needles using quantum critical chains. The agreement between numerical results performed on critical transverse field Ising model and XX chain with our exact results is very good. We also comment on the mutual R\'enyi information of two disjoint intervals.
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Cited by 1 Pith paper
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Emptiness formation probability and Painlev\'e V equation in the XY spin chain
The emptiness formation probability of the XY chain, in the double-scaling limit near its critical lines, is governed by a Painleve V tau function; the result is exact at the Ising point and numerically supported elsewhere.
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