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.
Benjamin works in the area of many-body localization and quantum computing. 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.
More recently, Benjamin has been tackling the transition between the MBL and ergodic phases. He has shown that there are universal aspects of the mutual information that show up in this transition.
In addition to Benjamin's work on MBL, Benjamin has been heavily involved in developing efficient classical simulators of quantum computers by using tensor network methodologies.
Eli works on machine learning and inverse problems. He has developed a new efficient algorithm, the eigenstate to Hamiltonian construction (EHC) which takes a wave-function and finds all the local parent Hamiltonians. More recently, Eli has been considering how this work can be generalized for other areas of input.
Eli got a 2017 NSF Grad Fellowship Honorable Mention as well one of the departments Scott Anderson Outstanding Graduate Assistant Awards for 2017.
Ryan works in strongy correlated systems and entanglement transitons. Ryan developed a new methodology to help minimize the effect of the sign problem by optimizing over a set of basis. Amazingly enough, even though you can't measure how bad the sign problem is (without beating down a sign problem), Ryan can still efficiently optimize on large systems
Ryan has also been working on random tensor networks, pair density waves and superconductivity. Ryan has also been making significant improvements to our group's variational Monte Carlo and DMRG research codes.
Di has worked in the areas of many-body localization, machine learning, and quantum computing.
In the area of many-body localization, Di has shown one of the first concrete models of a eigenstate phase which goes beyond the many-body localized phase. Concretely, the spin-disordered Hubbard model has both area law and log-law eigenstates.
In machine learning, Di has recently developed the neural net backflow. The neural net backflow is a new variational ansatz for using neural nets with fermions.
Gabi is working on matrix product states for spin liquids.
Abid is working on machine learning experimental data and MERA networks.
Chad is working on spin-liquids.
Lucas is working on quantum computing
James is working on spin-liquids.
Greg is working on quantum computing and many-body localization.
Dmitrii's thesis focused on two majors areas: frustrated magnetism and machine learning. In addition, Dmitrii developed a number of major research codes including our groups highly parallelized exact diagonalization code which we run on Blue Waters and a GPU based variational Monte Carlo code built on top of tensorflow.
Dmitrii was part of a team that found the "mother" of all phases on the kagome lattice - a simple macroscopically degenerate Hamiltonian which Dmitrii showed is connected to a panoply of phases including the celebrated kagome Heisenberg (KAHF) spin-liquid. He also showed that the KAHF is very close (maybe at) a critical point between the spin liquid and another phase.
Dmitrii's second foray into frustrated magnetism was to tackle the quantum phase diagram of the spin one-half stuffed honeycomb lattice. Tuning two parameters in this phase diagram results in nine different phases making it one of the richest quantum phase diagrams I know about. One of these phases is a spin-liquid.
In the area of machine learning, Dmitrii made a number of key contributions. To begin with, he developed a paradigm, computational graph states for representing any computer program as a variational wave-function. Over the century of the variational approach, ansatz have become more general with more parameters. Computational graph states fulfill this progression as the most general possible ansatz.
Dmitrii's second major `machine learning' contribution was developing a new variational optimization approach, supervised wave-function optimization (SWO) inspired by the ideas of supervised learning. Typically, we optimize in variational Monte Carlo by taking steps which minimize the energy. Instead in SWO,we optimize to target to match the fidelity against an already existing wave-function. This really opens up a whole family of optimization techniques. One technique in this family replicates imaginary time evolution in a more efficient and numerically stable approach.
In the process of this work, Dmitrii tested a large number of new ansatz. While many of them are competitive with the state of the art, one of the most conceptually interesting is the convolution neural net wave-function. It turns out that this wave-function can be trained on one system size ($N=40$) and then naturally generalizes to other system sizes without changing any parameters. This gives essentially a ansatz in the thermodynamic limit in the same spirit as imps and ipeps.
Finally, Dmitrii did a lot of analysis looking at how quickly neural net wave-functions approach the true ground state as you increase the total number of neurons as well as understanding the interaction of the sign structure with this effect.
Dmitrii has won the physics departments Jordan Asketh Award, which recognizes one of the year’s outstanding European graduate students.
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.
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 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 then did a postdoc at Johns Hopkins and is currently faculty at Florida State University. 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 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.