High-Order Coupled Cluster Method Applied to Lattice Quantum Spin Systems

  • 1 February 2023
  • 13:00 - 14:00
  • DAV029

Presented by Dr Damian JJ Farnell from Cardiff University UK.

Relevant paper:

Farnell, Damian JJ, J. Schulenburg, J. Richter, and K. A. Gernoth. "High-order coupled cluster calculations via parallel processing: An illustration for CaV 4 O 9." Physical Review B 72, no. 17 (2005): 172408.

 In the first part of the talk, we will explore the Coupled Cluster Method (CCM), a powerful and versatile method of quantum-many-body theory. Taking lattice spin Hamiltonians as a starting point, I will show how the CCM can be applied to low orders of approximation to study the zero-temperature properties of the ground and excited states of these systems. Intensive computing resources in order to carry out exactly the same calculations, albeit to much higher orders of (localised) approximation. I use the computer code https://www-e.uni-magdeburg.de/jschulen/ccm/ written by Farnell and Schulenburg (amongst others). I will present typical results for Archimedean lattice Heisenberg antiferromagnets (HAFs) to show the (reasonable) accuracy of the method for two dimensional spatial lattices. I will show that the CCM is particularly useful for mapping out phases diagrams of highly "frustrated" systems, especially in 2D and 3D dimensions, and present results for the spin-half "J1-J2 model" on the square lattice as an example. Finally, I will show that the CCM can provide excellent quantitative correspondence for spin-plateau for the spin-half and spin-one triangular lattice HAFs in the presence of an external magnetic field when compared to experimental results. Finally, I will present an analysis of the pros and cons of high-order CCM before moving on to possible future research.
 
I work in the school of dentistry at Cardiff university and am the school lead for the dental data science research group. Quantum spins are actually my "hobby"... My experience (over 22 years now amazingly) is that there are many opportunities to use mathematics, physics, and computing in medicine and dentistry, e.g.: from teaching students "how to read a paper" (a crucial part of evidenced-based medicine -- mostly stats and experimental design), to using biostatistics and / or data science (in epidemiology / public health, clinical audits, and research etc.), as well as numerical biosimulations and computational biology (e.g., Monte Carlo eye colour simulation after treatment by a topical drug for glaucoma), and in medical imaging and image / signal processing. I think that there is probably also a massive unmet need in medicine and dentistry for numerate and computer literate researchers. I (very briefly) present my journey from spins to dental data science, before listing a few current research projects (that should appeal to physicists), before going on to list some of the challenges (and rewards!) of medical and dental research.
 
 
 IMPORTANT:
  • Attendance of the Landau seminar series is compulsory for Physics PhD students.
  • Taking part in discussions or Q&As during or after the seminar is equally important and essential part of your PhD training
 

In the first part of the talk, we will explore the Coupled Cluster Method (CCM), a powerful and versatile method of quantum-many-body theory. Taking lattice spin Hamiltonians as a starting point, I will show how the CCM can be applied to low orders of approximation to study the zero-temperature properties of the ground and excited states of these systems. Intensive computing resources in order to carry out exactly the same calculations, albeit to much higher orders of (localised) approximation. I use the computer code https://www-e.uni-magdeburg.de/jschulen/ccm/ written by Farnell and Schulenburg (amongst others). I will present typical results for Archimedean lattice Heisenberg antiferromagnets (HAFs) to show the (reasonable) accuracy of the method for two dimensional spatial lattices. I will show that the CCM is particularly useful for mapping out phases diagrams of highly "frustrated" systems, especially in 2D and 3D dimensions, and present results for the spin-half "J1-J2 model" on the square lattice as an example. Finally, I will show that the CCM can provide excellent quantitative correspondence for spin-plateau for the spin-half and spin-one triangular lattice HAFs in the presence of an external magnetic field when compared to experimental results. Finally, I will present an analysis of the pros and cons of high-order CCM before moving on to possible future research.

I work in the school of dentistry at Cardiff university and am the school lead for the dental data science research group. Quantum spins are actually my "hobby"... My experience (over 22 years now amazingly) is that there are many opportunities to use mathematics, physics, and computing in medicine and dentistry, e.g.: from teaching students "how to read a paper" (a crucial part of evidenced-based medicine -- mostly stats and experimental design), to using biostatistics and / or data science (in epidemiology / public health, clinical audits, and research etc.), as well as numerical biosimulations and computational biology (e.g., Monte Carlo eye colour simulation after treatment by a topical drug for glaucoma), and in medical imaging and image / signal processing. I think that there is probably also a massive unmet need in medicine and dentistry for numerate and computer literate researchers. I (very briefly) present my journey from spins to dental data science, before listing a few current research projects (that should appeal to physicists), before going on to list some of the challenges (and rewards!) of medical and dental research.

 

IMPORTANT:

  • Attendance of the Landau seminar series is compulsory for Physics PhD students.
  • Taking part in discussions or Q&As during or after the seminar is equally important and essential part of your PhD training

Please forward to anyone interested.

 

 

 

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