p848ps3 - Physics 848 Problem Set 3 Due Thursday October 27...

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Unformatted text preview: Physics 848: Problem Set 3 Due Thursday, October 27 at 11:59 PM Note: each problem is worth 10 points unless otherwise stated. 1. Consider the anisotropic spin-1/2 Heisenberg model , with Hamiltonian given by H =- J k X h ij i S iz S jz- 1 2 J ⊥ X h ij i ( S i + S j- + S i- S j + ) . (1) Here S i + , S i- , and S iz are the raising, lowering, and z-component of the spin operators for a spin-1/2 particle, as defined in class, J k and J ⊥ are positive interaction energies, and the sums run over distinct pairs of nearest neighbor sites. (a). What is the ground state of this system, assuming that J k > J ⊥ ? Using the same approach as that done in class, obtain the spectrum for spin waves on a simple cubic lattice. Show that when J | = J ⊥ , this spectrum reduces to that of the isotropic spin-1/2 Heisenberg model on a simple cubic lattice (also obtained in class). 2. Consider the isotropic spin-1/2 Heisenberg model, for which the Hamil- tonian is given by eq. (1) above with J k = J...
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This note was uploaded on 07/17/2008 for the course PHYS 848 taught by Professor Stroud during the Fall '05 term at Ohio State.

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p848ps3 - Physics 848 Problem Set 3 Due Thursday October 27...

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