Yang Xian
Research Interests
My main research interest is in the area of quantum many-body
theories and their applications in condensed matter physics, particularly
in quantum spin lattices and strongly correlated boson and fermion
systems. Quantum many-body theories study correlation effects of
interacting quantum particles in their ground and excited states. This
field of theoretical physics therefore covers a wide range of physical
systems, from atoms and molecules (many-electron systems), nuclei and nuclear matters
(many-nucleon systems), to low-temperature gases, liquids, solids and artificial systems
such as quantum dots. A microscopic quantum many-body theory usually takes
a Hamiltonian approach, evaluating physical quantities (such as the binding energy of an atom,
order parameter of a spin lattice, excitation spectra of a quantum fluid) by ab initio
calculations using well-developed techniques, including analytical
(perturbational/variational/diagramatic)
methods and computer simulations. Despite tremondous progress over the last five
decades in both analytical and computational aspects, there remain
challenges in the field of microscopic quantum many-body theories: we still
have difficulties in dealing with the strongly correlated fermion systems
with strong spin fluctuations, typified in high-temperature superconductors and
helium-3 superfluids; accurate calculations are still limited to small molecules, etc.
Breakthroughs in both our analytical skills and computational power are still needed.
Research projects:
- A general microscopic technique based on a localised
approximation of the coupled-cluster method (CCM, a powerful technique widely used
in atoms, molecules and finite nuclei) for accurate calculations of
ground state energy, order parameter and other properties of
Hamiltonian lattice systems (spin/electron lattices, lattice gauge theories).
- Exact calculations on infinite one-dimensional quantum spin
lattices using Bethe ansatz and other methods.
- Microscopic many-body theory of dimerised spin lattice
systems based on composite spin operators for investigation of quantum fluctuations
due to different resonating valence bond configurations.
- One of my current focuses is the variational CCM and its unification with the variational Jastrow theory.
The variational CCM is an extension of the traditional CCM to a variational formalism and the
Jastrow theory is one of only few methods capable of dealing with strong correlations.
Unification of these two methods combines their advantages to overcome the obstacles arised by using
one method alone - the difficulties of dealing with strong correlations by CCM and of dealing with
strong spin fluctuations by Jastrow theory. I am particularly interested in application of this
unified approach (developed here at Manchester) to strongly correlated boson and fermion systems such as
recently discovered quantum spin liquid RuCl3 and superconducting twisted bilayered graphene.
- I am also interested in quatitative study of topological properties (including calculations of thermal Hall effects) of
layered magnetic systems such as recently synthesized chromium trihalides. The aim here is to provide
quantative support for development of magnon-based devices.
Main and recent publications:
- Mohammd Merdan and Y. Xian, "The effects of three magnons interactions in the magnon-density waves of triangular spin lattices",
arXiv:1901.11007,
Journal of Low Temperature Physics 197, 81-94 (2019).
- Christian Moulsdale, Pierre A. Pantaleon, Ramon Carrillo_Bastos, and Y. Xian, "Unconventional Thermal Hall Effect in a
Coupling Modulated Honeycomb Topological Magnon Insulator",
arXiv:1901.09213, Phys. Rev. B 99, 214424 (2019).
- Pierre A. Pantaleon, Ramon Carrillo_Bastos, and Y. Xian, "Topological Magnon Insulator with a Kekule Bond Modulation",
arXiv:1809.01073, J. Phys.: Condend. Matter 31, 085802 (2019).
- Pierre A. Pantaleon and Y. Xian, "Edge on-site potential effects in a honeycomb topological magnon insulator",
arXiv:1801.09945
, J. Phys. Soc. Japan 87, 064005 (2018).
- Pierre A. Pantaleon and Y. Xian, "Edge states in a ferromagnetic honeycomb lattice with armchair boundaries",
Physics B: Condensed Matter 530, 191 (2018).
- Pierre A. Pantaleon and Y. Xian, "Analytical study of the edge states in the bosonic Haldane model",
arXiv:1704.07746v2
, J. Phys.: Condens. Matter 29, 295701 (2017).
- Wissam A. Ameen, Niels R. Walet and Y. Xian, "Electronic correlations in the Hubbard model on a bi-partite lattice",
arXiv:1510.08751v2,
Annals of Physics 378, 280 (2017).
- Y. Xian and Mohammad Merdan, "Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices",
Journal of Physics: Conference Series Vol. 529, Page 218
(arXiv:1312.4929), 2014.
- Mohammd Merdan and Y. Xian, "Excited states of the quasi-one-dimensional hexagonal quantum antiferromagnets",
arXiv:1212.5924,
Phys. Rev. B 87, 174434 (2013).
- Mohammd Merdan and Y. Xian, "Longitudinal excitations in triangular lattice antiferromagnets",
DOI 10.1007/s10909-012-0778-1, J. of Low Temp. Phys. 171, 797 (2012).
- Mohammad Merdan and Y. Xian, "Coupled-cluster calculations for the ground- and excited-states
of the spin-half XXZ model", J. Phys.: Conden. Matter 23,
406001 (2011).
- Y. Xian, "Longitudinal excitations in quantum antiferromagnets", J. Phys.: Conden. Matter 23,
346003 (2011).
- Y. Xian, "Variational Jastrow coupled-cluster theory of quantum many-body systems",
Phys. Rev. A 77,
042103 (2008).
- Y. Xian, "Excited states of quantum many-body interacting systems: A variational
coupled-cluster description", J. Phys.: Condens. Matter 19,
216221 (2007).
- Y. Xian, "Diagrammatic approach in the variational coupled-cluster method",
Phys. Rev. B 72,
224438 (2005).
- Y. Xian, "Extension of the coupled-cluster method: a variational formalism",
Phys. Rev. B 66,
184427-33 (2002).
- R.F. Bishop, Y. Xian, and C. Zeng, "A microscopic coupled-cluster treatment
of electronic correlations in Hubbard models", Int. J. Quantum Chem. 55, 181-6 (1995).
- Y. Xian, "Theory of valence-bond lattice on spin-lattices", in
Condensed Matter Theories 10 (eds. M. Casa, M. de Llano, J. Navarro, and A. Polls),
Nova, New York, 541-61 (1995).
- R.F. Bishop, R.G. Hale, Y. Xian, "Systematic Inclusion of high-order multispin
correlations for the spin-1/2 XXZ models", Phys. Rev. Lett. 73, 3157-60 (1994).
- Y. Xian, "A microscopic approach to the dimerization in frustrated spin-1/2
antiferromagnetic chains", J. Phys.: Condens. Matter 6, 5965-80 (1994).
- Y. Xian, "Exact results of dimerization order parameter in SU(n)
antiferromagnetic chains", Phys. Lett. A 183, 437-40 (1993).
- R.F. Bishop, A.S. Kendall, L.Y. Wong, and Y. Xian, "Correlations in Abelian lattice gauge
field model: A microscopic coupled-cluster treatment", Phys. Rev. D 48, 887 (1993).
- R.F. Bishop, J.B. Parkinson, and Y. Xian, "Coupled-cluster treatments of
correlations in quantum antiferromagnets", Phys. Rev. B 44, 9425-43 (1991).
A complete list of publications can be found
here.
Teaching
2008/09:
- PHYS 20352 Thermal and Statistical Physics
- PHYS 30602 Quantum Mechanics of Atoms and Molecules
2009/10:
- PHYS 20352 Thermal and Statistical Physics
2010/11:
- PHYS 20352 Thermal and Statistical Physics
- PHYS 40131 Research Masterclass (coordinator)
2011/12:
- PHYS 20352 Thermal and Statistical Physics
2012/13:
- PHYS 20352 Thermal and Statistical Physics
(Website)
- 3rd Year Example Class: General Physics
Booklet
2013/14, 2014/15, 2015/16, 2016/17, 2017/18, 2018/19:
- PHYS 20101 Introduction to Quantum Mechanics
(Notes are online on TeahWeb and on Blackboard)
- PHYS 40202 Advanced Quantum Mechanics
(Website and more materials on Blackboard)
- PHYS30880 BSc Dissertation
- PHYS30811 2nd Vacation Essay
May 2019