# Phase Transition in the Density of States of Quantum Spin Glasses

@inproceedings{ErdHos2014PhaseTI,
title={Phase Transition in the Density of States of Quantum Spin Glasses},
author={L'aszl'o ErdHos and Dominik Schr{\"o}der},
year={2014}
}
• Published 6 July 2014
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We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of [6] that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform…
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## References

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We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number
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Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We
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We prove that translationally invariant Hamiltonians of a chain of n qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit {n \rightarrow
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Here I = S j (a2j 1,a2j) andI(y) is the characteristic function of the set I. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in I is equal to �(a). Also �(a) is a
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We consider an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density. Both "spinglass" and ferromagnetic
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In this paper we study the enumeration of diagrams of n chords joining 2n points on a circle in disjoint pairs. We establish limit laws for the following three parameters: number of components, size
The statistical properties of the characteristic values of a matrix the elements of which show a normal (Gaussian) distribution are well known (cf. [6] Chapter XI) and have been derived, rather