A numerical approach for calculating exact non-adiabatic terms in quantum dynamics

Ewen D.C. Lawrence; Sebastian F.J. Schmid; Ieva Čepaitė; Peter Kirton; Callum W. Duncan

doi:10.21468/SciPostPhys.18.1.014

A numerical approach for calculating exact non-adiabatic terms in quantum dynamics

Ewen D.C. Lawrence, Sebastian F.J. Schmid, Ieva Čepaitė, Peter Kirton, Callum W. Duncan

Physics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

13 Downloads (Pure)

Abstract

Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.

Original language	English
Article number	014
Journal	SciPost Physics
Volume	18
Issue number	1
DOIs	https://doi.org/10.21468/SciPostPhys.18.1.014
Publication status	Published - 14 Jan 2025

Funding

The authors acknowledge K. Damezin, P. Claeys, S. Morawetz, and A. Polkovnikov for useful discussions. The data for this manuscript is available at Ref. [79]. E.D.C.L acknowledges funding from EPSRC grant EP/T517938/1. C.W.D. acknowledges funding from EPSRC grant EP/Y005058/1.

Keywords

quantum dynamics
quantum technologies
adiabatic gauge potential
non-adiabatic terms

Access to Document

10.21468/SciPostPhys.18.1.014Licence: CC BY 4.0

Lawrence-etal-2025-SciPostPhys-A-numerical-approach-for-calculating-exact-non-adiabatic-terms-in-quantum-dynamicsFinal published version, 2.38 MBLicence: CC BY 4.0

https://scipost.org/submissions/2401.10985v2/

Cite this

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abstract = "Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.",

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N2 - Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.

AB - Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.

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A numerical approach for calculating exact non-adiabatic terms in quantum dynamics

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