Group

Bryan Clark

Email: bkclark@illinois.edu
Office: 2111 ESB

I am an assistant professor at the University of Illinois and have the opportunity to collaborate with many talented and passionate graduate students and postdocs.



Graduate Students


Dmitrii Kochkov
Dmitrii works in the area of frustrated magnetism. Methodologically, he is an expert in exact diagonalization and variational approaches. He has developed our group's massively parallel exact diagionalization code which we run on Blue Waters.

Dmitrii's recent work has made an important contribution to the understanding of phases on the kagome lattice. He showed that there is a macroscopically degenerate point on the kagome lattice which is connected (or very close to) the spin-liquid at the Heisenberg point (KAHF) as well as many of the ordered phases on the kagome lattice. In addition, Dmitrii has made a compelling case that the KAHF is actually a critical point between two spin-liquids.

More recently, Dmitrii has been thinking about the phase diagram of the stuffed honeycomb lattice which he spoke about at the most recent March Meeting.

Dmitrii has won the physic departments Jordan Asketh Award, which recognizes one of the year’s outstanding European graduate students.


Benjamin Correa
Benjamin works in the area of many-body localization. In a recent work, Benjamin used SIMPS to comprehensively compute properties of MBL eigenstates below the mobility edge. The fact that Benjamin showed SIMPS works underneath the mobility edge is one of the most compelling arguments for the existence of a mobility edge. One of the most exciting results of Benjamin's work was showing that MBL eigenstates know that they are sitting underneath a mobility edge. Benjamin also found that the eigenstates of the single-particle density matrix is largely universal over all states in the eigenspectrum of the MBL Hamiltonian.

In addition to this work, Benjamin has worked on developing algorithms to probe the MBL phase in two-dimensions.


Jahan Claese
Jahan recently has published a paper which generalizes the variational Monte Carlo approach to finite temperature. This generalization allows us to use, at finite temperature, the full machinery of variational wave-functions that have been developed over the last thirty years.

More recently, Jahan has been thinking about problems in quantum information.

Jahan received an Honorable Mention in the NSF graduate research fellowship program.


Eli Chertkov
Eli is interested in machine learning and inverse problems. Eli got a 2017 NSF Grad Fellowship Honorable Mention as well one of the departments Scott Anderson Outstanding Graduate Assistant Awards for 2017.


Ryan Levy
Ryan has recently joined the group. He is interested in superconductivity and algorithms for fermions and has been making significant improvements to our group's variational Monte Carlo research code.


Di Luo
Di Luo has recently joined the group. He is interested in improved variational ansatz as well as many-body localization.


Abid Khan
Abid Khan has recently joined the group and is interested in neural networks.



Alumni


Xiongjie Yu (former student)
Xiongjie's thesis focused on many-body localization and Xiongjie was involved in five papers as part of his graduate work (with a few more still coming out). In his published work, Xiongjie made two important methodological developments:

  • SIMPS: An algorithm which finds the eigenstates in the middle of the spectrum of a many-body localized phase in a matrix-product state representation. This allows access to see eigenstates of size L>64.
  • The cut-averaged entanglement entropy (CAEE): If you measure the entanglement of different cuts in a disordered-interacting system, the amount of entanglement you see will jump around with the cut (because of the disorder). This means that it's very hard to look at one disordered-sample and decide if it's obeying an area-law or volume-law. In Xiongjie's paper, he showed that, by sub-additivity of entanglement, if you average over all the cuts of a fixed subsystem size the entanglement curve S(La) is convex. This means you can look at one disordered sample and see a smooth entanglement curve!

Using SIMPS, Xiongjie has shown for large systems that entanglement saturates as a function of system size, that ETH breaks down and how to build many local excitations. In addition, Xiongjie collaborated on a comprehensive work using SIMPS to look at the properties of the one-body density matrix in the mobility edge.

Using CAEE, Xiongjie has found bimodality of entanglement in the MBL critical region as well as identified a universal one-parameter family of curves in this region.

In addition to these works Xiongjie also looked at an eigenstate phase transition in MBL in a random energy model finding the first instance where the finite size transition to the ergodic phase happens from the MBL side; he also looked at twist defect chains at criticality.

Xiongjie chose to go into industry and now works at Akuna Capital.


Michael Kolodrubetz (former student)
As a graduate student at Princeton, Michael was (unofficially) co-advised by myself and David Huse. Since then he has gone on to postdocs with Anatoli Polkovnikov and Anders Saandvik at Boston University and then Joel Moore at UC Berkeley. Most recently, Michael has become faculty at UT Dallas.

Michael is an expert on quantum dynamics and interacting with experimentalists. In his thesis, Michael developed new versions of FCIQMC, including partial-node FCIQMC; showed in what cases the fermion sign problem is affected by moving from first to second quantization; and worked on numerous projects looking at critical scaling in dynamic quantum systems.


Hitesh Changlani (former postdoc)
Hitesh was a graduate student with Chris Henley at Cornell University and a postdoc with myself, David Ceperley, Lucas Wagner and Shinshei Ryu at UIUC (he is a prolific collaborator). Hitesh has moved now to a postdoc at Johns Hopkins. He is an expert in, among other things, frustrated magnetism and downfolding.

One project he worked on with me is the development of new methodological approaches for combining quantum Monte Carlo and DMRG. These new approaches allow us to go beyond what can be computed with either method individually.

More recently, Hitesh has discovered a new chiral spin liquid phase in the the 2/3 magnetic plateau on the kagome lattice as well as the existence of a macroscopically degenerate point which likely controls much of the physics on frustrated magnets on lattices of triangles.


David Luitz (former postdoc)
David Luitz was a graduate student with Fakher Assad, a postdoc with Fabien Alet and was an ICMT postdoc at University of Illinois. David Luitz is now in Munich as a Marie Skłodowska Curie Fellow. He works on entanglement and many-body localization. In our group he has found bimodality of entanglement in the MBL critical region as well as identified a universal one-parameter family of curves in this region.


Copyright © Bryan Clark 2016