Volume 89, Number 4, February 2010
|Number of page(s)||6|
|Published online||03 March 2010|
Energy gaps in quantum first-order mean-field–like transitions: The problems that quantum annealing cannot solve
LPTENS; CNRS et ENS UMR 8549 - 24 rue Lhomond, 75231 Paris Cedex 05, France, EU
2 PCT, UMR 7083 Gulliver; CNRS; ESPCI ParisTech - 10 rue Vauquelin, 75005 Paris, France, EU
3 Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory Los Alamos, NM 87545 USA
4 PMMH, UMR 7636; CNRS; ESPCI ParisTech - 10 rue Vauquelin, 75005 Paris, France, EU
Corresponding author: email@example.com
Accepted: 28 January 2010
We study first-order quantum phase transitions in models where the mean-field treatment is exact, and in particular the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing.
PACS: 05.30.-d – Quantum statistical mechanics / 05.70.Fh – Phase transitions: general studies
© EPLA, 2010
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