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A routine internet search for introductory material comes up with several possibilities. If you merely wish to read about the ideas in these topics you may not need any mathematics at all. eg "String Theory and Quantum Gravity for Dummies" in the "Dummies" Series. Also the more academic but briefer introduction : "Quantum Gravity for Dummies" http://arxiv....

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0) Note that in general, there is no need for the lattice spacings in different direction to be the same, as long as they all go to zero in the continuum limit. We can, for example, take the lattice spacing in the $x$ direction to be $a$, and the spacing in the $y$ direction to be $2a$. This is frequently done to achieve better resolution without the ...

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An approach to define the entanglement between identical particles, is to use the so-called geometric idea. For example, the generic wave function of a fermionic system is not a Slater determinant. However, since the simplest wave function for a fermionic system is a Slater determinant, we can quantify the entanglement between the identical fermions by ...

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Yes, this can be done as an application of the transfer matrix'' method. You can, for example, find an explicit computation for the XY model (N=2) in the book The theory of magnetism II: Thermodynamics and Statistical Mechanics by Daniel Mattis (p. 75 ff.). Another reference, in which the general case is treated, is Section 9.2 in the book Elements of ...

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