# Phase transition in the density of states of quantum spin glasses

Erdös L, Schröder DJ. 2014. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 17(3–4), 441–464.

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Author

Erdös, László

^{ISTA}^{}; Schröder, Dominik JDepartment

Abstract

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 Keating et al. (2014) 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 hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n1/2 we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.

Publishing Year

Date Published

2014-12-17

Journal Title

Mathematical Physics, Analysis and Geometry

Volume

17

Issue

3-4

Page

441 - 464

IST-REx-ID

### Cite this

Erdös L, Schröder DJ. Phase transition in the density of states of quantum spin glasses.

*Mathematical Physics, Analysis and Geometry*. 2014;17(3-4):441-464. doi:10.1007/s11040-014-9164-3Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses.

*Mathematical Physics, Analysis and Geometry*. Springer. https://doi.org/10.1007/s11040-014-9164-3Erdös, László, and Dominik J Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.”

*Mathematical Physics, Analysis and Geometry*. Springer, 2014. https://doi.org/10.1007/s11040-014-9164-3.L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,”

*Mathematical Physics, Analysis and Geometry*, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.Erdös, László, and Dominik J. Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.”

*Mathematical Physics, Analysis and Geometry*, vol. 17, no. 3–4, Springer, 2014, pp. 441–64, doi:10.1007/s11040-014-9164-3.**All files available under the following license(s):**

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