Phase transition in the density of states of quantum spin glasses

L. Erdös, D.J. Schröder, Mathematical Physics, Analysis and Geometry 17 (2014) 441–464.


Journal Article | Published | English
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;
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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
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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/s11040-014-9164-3
Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry, 17(3–4), 441–464. https://doi.org/10.1007/s11040-014-9164-3
Erdös, László, and Dominik J Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry 17, no. 3–4 (2014): 441–64. 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, pp. 441–464, 2014.
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.
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.

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