Phase transitions and gaps in quantum random energy models
arXiv:1002.4409 · doi:10.1016/j.physa.2018.09.193
Abstract
By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and continuous. We rigorously establish the existence of a universal first order quantum phase transition, obeyed by both the ground and the first excited states. The presence of an exponentially vanishing minimal gap at the transition is general but, quite interestingly, the gap averaged over the realizations of the random potential is finite. This fact leaves still open the chance for some effective quantum annealing algorithm, not necessarily based on a quantum adiabatic scheme.
8 pages, 4 figures
References in corpus (5)
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
- Simple Glass Models and their Quantum Annealing
- Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
- Exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit