## Research

Research in our group centres on developing microscopic theories for a variety of phenomena relating to the electronic and magnetic properties of condensed matter. This encompasses both the vast world of the solid state, be it crystalline or amorphous, as well as topical nanoscale systems such as quantum dots and molecular electronic devices. The work is very much interdisciplinary, straddling the borders of chemistry and physics.

The essential theoretical theme throughout is that of quantum many-body theory: the quantum and statistical mechanics of ~10^{23} interacting electrons. Our interests centre on *strongly correlated systems*, where physical properties are dominated by strong electron interactions; as well as *disordered* interacting systems where the additional, subtle effects of disorder come into play.

The problem of strongly interacting electrons has been around for more than half a century. It is one of the most challenging and active fields in condensed matter science, and an understanding of it underpins an enormous range of phenomena. This includes metal-insulator transitions – one example of a so-called quantum phase transition, in this case between an insulating and metallic state and induced, for example, by increasing the pressure of a system; quantum magnetism, whether of intrinsically localised spins or in itinerant electron systems; high-temperature superconductivity; the behaviour of magnetic impurities in non-magnetic metals or insulators; and the physical properties of f-electron materials such as heavy Fermion metals or Kondo insulators. Strong electron correlations also play a key role in the electrical transport properties of quantum dots – the single-electron transistor for example – and likewise in the field of molecular electronics.

For *disordered* and interacting many-body systems, a whole new raft of potential complexity arises; including the phenomenon of many-body localisation, whereby disorder and/or interactions can drive an isolated quantum system into a non-ergodic, localised phase, whose very existence represents a fundamental failure of equilibrium statistical mechanics.

How then does one tackle such problems? So-called *ab initio* calculations are out of the question: even if computers could deal with anywhere near ~10^{23} interacting electrons, one would learn only what the "answer" is, and not why - a far more interesting question. The modus operandi is to develop and study the simplest theoretical models that capture the essential physical behaviour one seeks to understand. But "simplest" is a misnomer: the relevant models are rarely soluble; and one seeks to construct approximate but physically motivated theories, employing a variety of theoretical and computational methods from several areas of condensed matter science, and developing new approaches in the process.

Prospective students may have a background in either chemistry or physics: the work is adaptable to students from different backgrounds, and its intrinsic interdisciplinary nature means that each learns aspects of the other’s trade.

For further information about the members and research activities of the full Oxford Theoretical Chemistry Group, follow this link:

We also have strong links to, and are affiliated with, the Condensed Matter Theory group in Theoretical Physics at Oxford – for further details, follow this link:

http://www-thphys.physics.ox.ac.uk/research/condensedmatter/home.html

## Selected Publications

*Fock-space correlations and the origins of many-body localisation, *S. Roy and D. E. Logan,

*Phys. Rev. **B ***101**, 134202 (2020). Editors' Suggestion.

*Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions, *

S. Roy and D. E. Logan,* SciPost Phys., ***7**, 042 (2019).

*Percolation in Fock space as a proxy for many-body localization, *

S. Roy, J. T. Chalker and D. E. Logan,* Phys. Rev. B ***99**, 104206 (2019). Editors' Suggestion.

*Exact solution of a percolation analog for the many-body localization transition, *

S. Roy, D. E. Logan and J. T. Chalker,* Phys. Rev. B ***99**, 220201 (R) (2019).

*Many-body localization in Fock space: A local perspective,*

D. E. Logan and S. Welsh,* Phys. Rev. B ***99 **, 045131 (2019).

*Simple probability distributions on a Fock-space lattice*,

S. Welsh and D. E. Logan, *J. Phys.: Condensed Matter ***30**, 405601 (2018).

*Mott transitions in the periodic Anderson model*,

D. E. Logan, M. R. Galpin and J. Mannouch, *J. Phys.: Condensed Matter ***28**, 455601 (2016).

*Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model*,

D. E. Logan and M. R. Galpin, *J. Phys.: Condensed Matter ***28**, 025601 (2015).

*Quasiparticle interference from magnetic impurities, *

P. G. Derry, A. K. Mitchell and D. E. Logan,* Phys. Rev. B ***92**, 035126 (2015).

*Multiple magnetic impurities on surfaces, *

A. K. Mitchell, P. G. Derry and D. E. Logan,* **Phys. Rev. B ***91**, 235127 (2015).

*Common non-Fermi liquid phases in quantum impurity physics, *

D. E. Logan, A. P. Tucker and M. R. Galpin. *Phys. Rev. B ***90**, 075150 (2014).

*Generalized Wilson chain for solving multichannel quantum impurity problems, *

A. K. Mitchell, M. R. Galpin, S. Wilson-Fletcher, D. E. Logan and R. Bulla, *Phys. Rev. B ***89**,

121105 (R) (2014).

*Conductance fingerprint of Majorana fermions in the topological Kondo effect, *

M. R. Galpin, A. K. Mitchell, J. Temaismithi, D. E. Logan, B. Beri and N. R. Cooper, *Phys. Rev. B *

**89**, 121105 (2014).

*Local Moment Formation and Kondo Screening in Impurity Trimers, *

A. K. Mitchell, T. F. Jarrold, M. R. Galpin and D. E. Logan, *J. Phys. Chem. B, ***117**, 12777 (2013).

*Tunable Kondo Physics in a Carbon Nanotube Double Quantum Dot, *

S. J. Chorley, M. R. Galpin, F. W. Jayatilaka, C. G. Smith, D. E. Logan and M. R. Buitelaar,

*Phys. Rev. Lett., ***109**, 156804 (2012).

*Two-channel Kondo physics in two-impurity Kondo models, *

A. K. Mitchell, E. Sela and D. E. Logan, *Phys. Rev. Lett, ***108**, 086405 (2012).

*Magnetic field effects in few-level quantum dots: Theory and application to experiment*,

C. J. Wright, M. R. Galpin and D. E. Logan, Phys. Rev. B **84**, 115308 (2011).

*Two-channel Kondo physics in tunnel-coupled double quantum dots*,

F. W. Jayatilaka, M. R. Galpin and D. E. Logan, *Phys. Rev. B ***84**, 115111 (2011).

*Two-channel Kondo physics in odd impurity chains, *

A. K. Mitchell, D. E. Logan and H. R. Krishnamurthy, *Phys. Rev. B ***84**, 035119 (2011).

*Two-channel Kondo phases and frustration-induced transitions in triple quantum dots*,

A. K. Mitchell and D. E. Logan, *Phys. Rev. B ***81**, 075126 (2010).

*Interplay between Kondo physics and spin-orbit coupling in carbon nanotube quantum dots*,

M. R. Galpin, F. W. Jayatilaka, D. E. Logan and F. B. Anders, *Phys. Rev. B ***81**, 075437 (2010).

*Tunneling transport and spectroscopy in carbon nanotube quantum dots*,

D. E. Logan and M. R. Galpin, *J. Chem. Phys. ***130**, 224503 (2009).

*Correlated electrons in two-level quantum dots: Phase transitions, transport, and experiment*,

D. E. Logan, C. J. Wright and M. R. Galpin, *Phys. Rev. B ***80**, 125117 (2009).

*A local moment approach to the degenerate Anderson model*,

M. R. Galpin, A. B. Gilbert and D. E. Logan, *J. Phys.: Condensed Matter ***21**, 375602 (2009).

*Quantum phase transition in quantum dot trimers*,

A. K. Mitchell, T. F. Jarrold and D. E. Logan, *Phys. Rev. B ***79**, 085124 (2009).

*Zero-bias conductance in carbon nanotube quantum dots*,

F. B. Anders, D. E. Logan, M. R. Galpin and G. Finkelstein, *Phys. Rev. Lett. ***100**, 086809 (2008).

*Optical and transport properties of paramagnetic Heavy Fermions: Theory compared to Experiment*,

D. E. Logan and N. S. Vidhyadhiraja, *J. Phys.: Condensed Matter ***17**, 2935 & 2959 (2005).

*Quantum phase transition in capacitively coupled double quantum dots*,

M. R. Galpin, D. E. Logan and H. R. Krishnamurthy, *Phys. Rev. Lett.* **94**, 186406 (2005).

*Dynamics and scaling in the Periodic Anderson Model*,

N. S. Vidhyadhiraja and D. E. Logan, *European Physical Journal *B **39**, 313 (2004).