Phase Diagram of the Quantum Random Energy Model

Abstract

We prove Goldschmidt's formula [Phys. Rev. B 47 (1990) 4858] for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is based on a combination of variational methods on the one hand, and percolation bounds on large-deviation configurations in combination with simple spectral bounds on the hypercube's adjacency matrix on the other hand.

arXiv comment12 pages, 1 figure

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Cited by in corpus (9)

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• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Spectral Analysis of the Quantum Random Energy Model
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams
• The Quantum Random Energy Model as a Limit of p-Spin Interactions
• The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model