Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions

Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibi...

Full description

Saved in:
Bibliographic Details
Published in:Physical review letters 2012-07, Vol.109 (3), p.030502, Article 030502
Main Authors: Laumann, C R, Moessner, R, Scardicchio, A, Sondhi, S L
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first-order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbor interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i) the QAA can be successful even across first-order transitions but also that (ii) it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.109.030502