Isotropic Entanglement

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One of the major problems hindering progress in quantum many body systems is the inability to describe the spectrum of the Hamiltonian. The spectrum corresponds to the energy spectrum of the problem and is of out-most importance in accounting for the physical properties of the system. A perceived difficulty is the exponential growth of the Hamiltonian with the number of particles involved. Therefore, even for a modest number of particles, direct computation appears intractable. This work offers a new method, using free probability and random matrix theory, of approximating the spectrum of generic frustrated Hamiltonians of arbitrary size with local interactions. In addition, we show a number of numerical experiments that demonstrate the accuracy of this method.