Skip to main content

Universal graph description for one-dimensional exchange models

Publication ,  Journal Article
Decamp, J; Gong, J; Loh, H; Miniatura, C
Published in: Physical Review Research
August 24, 2020

We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely, Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive crucial information about those models of fundamental importance in both classical and quantum physics, and to completely characterize their algebraic structure. Notably, we prove that the spectral gap can be obtained in polynomial computational time, which has strong implications in the context of adiabatic quantum computing with quantum spin chains. This quantity also characterizes the rate to stationarity of some important classical random processes such as interchange and exclusion processes. Reciprocally, we use results derived from the celebrated Bethe ansatz to obtain mathematical results about these graphs in the unweighted case. We also discuss extensions of this unifying framework to other systems, such as asymmetric exclusion processes- A paradigmatic model in nonequilibrium physics-or the more exotic non-Hermitian quantum systems.

Duke Scholars

Altmetric Attention Stats
Dimensions Citation Stats

Published In

Physical Review Research

DOI

ISSN

2643-1564

Publication Date

August 24, 2020

Volume

2

Issue

3

Related Subject Headings

  • 51 Physical sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Decamp, J., Gong, J., Loh, H., & Miniatura, C. (2020). Universal graph description for one-dimensional exchange models. Physical Review Research, 2(3). https://doi.org/10.1103/PhysRevResearch.2.033297
Decamp, J., J. Gong, H. Loh, and C. Miniatura. “Universal graph description for one-dimensional exchange models.” Physical Review Research 2, no. 3 (August 24, 2020). https://doi.org/10.1103/PhysRevResearch.2.033297.
Decamp J, Gong J, Loh H, Miniatura C. Universal graph description for one-dimensional exchange models. Physical Review Research. 2020 Aug 24;2(3).
Decamp, J., et al. “Universal graph description for one-dimensional exchange models.” Physical Review Research, vol. 2, no. 3, Aug. 2020. Scopus, doi:10.1103/PhysRevResearch.2.033297.
Decamp J, Gong J, Loh H, Miniatura C. Universal graph description for one-dimensional exchange models. Physical Review Research. 2020 Aug 24;2(3).

Published In

Physical Review Research

DOI

ISSN

2643-1564

Publication Date

August 24, 2020

Volume

2

Issue

3

Related Subject Headings

  • 51 Physical sciences