Research page

About

Here you can find details of my research and various projects I have been involved with.

I am interested many body quantum systems, numerical methods for their treatment and their possible applications in the realisation of quantum computing devices. Of particular interest to me are topological phases which were first discovered in the context of the Quantum Hall Effect. As well as being fascinating in their own right these phases are the essential ingredient for topological quantum computation.

Topological phases posses long range order but unlike other ordered phases, this order cannot be described by local order parameters. Instead this order is described by properties dependent on the topology of the system manifold, among which is the ground state degeneracy. An example of this is found in the toric code model. For this two dimensional model there is a single ground state when the system is realised on a plane and a four fold degenerate ground state when wrapped on a torus. Other characteristics of systems exhibiting topological phases are a robust spectral gap, critical edge modes described by conformal field theory, topological entanglement entropy and the more recently discovered signatures of topological order appearing in the entanglement spectrum.

The main focus of my research is currently on FQHE (fractional quantum hall effect) systems, spin chains and supersymmetric fermion models. For further information on my research please refer to publications listed below and my thesis which is online here. Also feel free to contact me with any questions or queries.

Publications

• Localization-enhanced and degraded topological-order in interacting p-wave wires
  G Kells, N Moran, D Meidan
  Phys. Rev. B 97. 095425 (2018). arXiv:1708.03758 (PDF)
• Trial wave functions for a Composite Fermi liquid on a torus
  M. Fremling, N. Moran, J. K. Slingerland, S. H. Simon
  Phys. Rev. B 97, 035149 (2018). arXiv:1711.01217 (PDF)
• Parafermionic clock models and quantum resonance
  N. Moran, D. Pellegrino, J. K. Slingerland, G. Kells
  Phys. Rev. B 95. 235127 (2017). arXiv:1701.05270 (PDF).
• Energy projection and modified Laughlin states.
  M. Fremling, J. Fulsebakke, N. Moran, J. K. Slingerland.
  Phys. Rev. B 93, 235149 (2016). arXiv:1601.06736 (PDF).
• Topological d-wave pairing structures in Jain states.
  N. Moran, A. Sterdyniak, I. Vidanovic, N. Regnault, M.V. Milovanovic.
  Phys. Rev. B 85. 245307 (2012) (PDF).
• Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality.
  L. Huijse, D. Mehta, N. Moran, K. Schoutens, J. Vala.
  New J. Phys. 14. 073002 (2012). (arxiv:1112.3314) (PDF).
• Exact ground states of a staggered super-symmetric model for lattice fermions.
  L. Huijse, N. Moran, J. Vala, K. Schoutens.
  Phys. Rev. B 84, 115124 (2011). (arxiv:1103.1368) (PDF).
• Diagonalisation of quantum observables on regular lattices and general graphs. Comp.
  N. Moran, G. Kells, J. Vala.
  Comp. Phys. Comm. 182, 1083-1092 (2011) (PDF).
• Valence bond states: link models.
  E. Rico, R. Hübener, S. Montangero, N. Moran, B. Pirvu, J. Vala, H.J. Briegel.
  Ann. Phys. 234, 1875-1896 (2009) (PDF).
• Finite size effects in the Kitaev honeycomb lattice model on a torus.
  G. Kells, N. Moran, J. Vala.
  J. Stat. Mech. P03006 (2009) (PDF).

Codes

In the course of my research I have written and been involved with the development of a number of numerical codes and utilities. What follows is a list and links to some that are freely available.

Hammer

Hammer is a set of numerical tools for treating systems of strongly interacting quantum many body systems and is aimed primarily at the study of Fractional Quantum Hall (FQH) systems. For more details visit the Hammer site.

HDF5Wrapper

This is a wrapper which aims at providing a simple interface for reading and writing data to HDF5 files. More details and the code are available on github at https://github.com/nmoran/HDF5Wrapper.

DiagHam

I am also a contributor to the DiagHam package nick-ux.lpa.ens.fr/diagham/wiki/.

DoQO

DoQO (Diagonalisation of Quantum Observables) is a numerical tool for the diagonalisation of observables of spin half and spinless fermionic systems which was developed during the course of my PhD. DoQO has many uses when studying quantum lattice models, quantum information and condensed matter systems. The main features are:

• Capability to diagonalise operators for arbitrary spin half and spinless fermionic systems.
• Designed to use large scale distributed memory machines (utilising PETSc and SLEPc).
• Capable of exploiting conservation and space group symmetries.

DoQO, as well as companion paper have been published in the Computer Physics Communications Program Library and can be found at the following links:

• Code: http://cpc.cs.qub.ac.uk/summaries/AEII_v1_0.html.
• Paper: Comp. Phys. Comm. 182, 1083-1092 (2011).

A more up to date version of the code can also be found on github at https://github.com/nmoran/DoQO.

Contact

Feel free to contact me at nmoran at thphys.nuim.ie if you would like to discuss any of these issues or just say hello.