Exact expression of the energy gap at first-order quantum phase transitions of the fully connected p-body transverse-field ising model with transverse interactions

Masaki Ohkuwa, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We study the energy gap between the ground state and the first excited state of a mean-field-type non-stoquastic Hamiltonian by a semi-classical analysis. The fully connected mean-field model with p-body ferromagnetic interactions under a transverse field has a first-order quantum phase transition for p ≥ 3. This first-order transition is known to be reduced to second order for p ≥ 5 by an introduction of antiferromagnetic transverse interactions, which makes the Hamiltonian non-stoquastic. This reduction of the order of transition means an exponential speedup of quantum annealing by adiabatic processes because the first-order transition is shown to have an exponentially small energy gap whereas the second order case does not. We apply a semi-classical method to analytically derive the explicit expression of the rate of the exponential decay of the energy gap at first-order transitions. The result reveals how the property of first-order transition changes as a function of the system parameters. We also derive the exact closed-form expression for the critical point where the first-order transition line disappears within the ferromagnetic phase. These results help us understand how the antiferromagnetic transverse interactions affect the performance of quantum annealing by controlling the effects of non-stoquasticity in the Hamiltonian.

Original languageEnglish
Article number114004
Journaljournal of the physical society of japan
Volume86
Issue number11
DOIs
Publication statusPublished - 2017 Nov 15

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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