Clark Research Group

Computational Condensed Matter

We are interested in (1) emergent quantum phenomena - how do the simple rules of quantum mechanics produce the rich dynamics and properties seen in quantum materials and devices; and (2) quantum computing - how do we use the power of quantum mechanics to compute faster then classical computers.

Our approach to these problems is driven largely through simulation. Simulation techniques in our toolbox include all forms of quantum Monte Carlo (PIMC, AFQMC, VMC,DMC), tensor networks (MERA,MPS,PEPS) and machine learning. Not only do we use known techniques, we regularly develop new algorithms broadening the horizon of what's possible.

I will be at KITP for a machine learning conference. Come find me and check out my student Di's poster on neural network backflow!

My student Eli will be at an Aspen conference on new methods. Ask him about his new algorithm, EHC, which eats wave-functions and produces Hamiltonians.

This semester, I will be teaching "Computing in Physics". I look forward to an exciting semester.

My student, Ryan, will be at the Florida summer school with a poster on pair density waves. Stop by and chat with him about his work if you're around.

This semester, I will be teaching "Computing in Physics". I look forward to an exciting semester.

My student, Ryan, will be at the Florida summer school with a poster on pair density waves. Stop by and chat with him about his work if you're around.

Much of our recent work on quantum dynamics has been in the area of *many body localization*.
When you put a coffee down on your desk, it cools down equilibrating to the temperature of the room.
But, there are generic quantum mechanical systems where thermalization breaks down -
the quantum equivalent of the never cooling coffee!

This realization has led to the discovery of a whole new category of phases - eigenstate phases - which are qualitiatively different from quantum phases. One of these phases - the many body localized phase - doesn't equilibrate, has weird entanglement in the eigenstates, and has weird eigenvalue statistics.

Some highlights of our work in this area include:

*a conceptual language for the MBL phase in terms of tensor networks;*

*scale invariance and bimodality of entanglement at the MBL-ergodic transition;*

*eigenstates in the mobility edge which know about the ergodic phase;*

*an eigenstate phase beyond the many-body localized phase;*

* new algorithms including SIMPS/ES-DMRG, for finding MBL eigenstates; an approach for finding compact
unitary matrix-product operators; and SCAEE, to determine the entanglement scaling for
one disorder realization.
*

To learn more about MBL + Tensor Networks, you might want to look at my talks from KITP (Nov. 2015), Perimeter (Oct. 2014) , or Dresden (May 2014) or MBL papers.

Quantum materials support a rich array of exotic phenomena such as superconductivity and heavy fermion behavior.
We've recently been interested in *frustrated magnets *- insulating materials with
magnetic spins living on lattices of triangles.

(Ferro)-magnetism has been known since the ancient Greeks. We now know that magnetism is a collective effect where a macroscopic number of spins align in the same direction. If instead, the spins are frustrated, no simple pattern of spins can can form and exotic phenomena such as spin-liquids can appear.

We have recently discovered a quantum (spin 1/2) Hamiltonian on the kagome lattice (corner sharing triangles) with exponential degneracy to which all phases on the kagome lattice seem to terminate. This replaces the former lore (classical frustration in the Ising limit) for why there is rich physics in frustrated systems with a more fundamental quantum understanding in terms of proximity to an exponentially degenerate Hamiltonian.

Another project has been searching for other simple Hamiltonians with exotic behavior. We've recently shown that the stuffed honeycomb lattice has a rich phase diagram supporting a multitude of classical and quantum phases including some interesting spin liquids phase(s).

We also work closely with experimentalists. A recent project has been working with Greg Macdougall on his spinel spin-ice.

To learn more about frustrated magnetism, see my talk at the Perimeter Institute on variational methods applied to the honeycomb and kagome lattice.

Most physical systems of sufficient complexity can simulate each other with only a polynomial slow-down. This is known as the extended Church Turing thesis. Bouncing billiard balls can compute anything your macbook can (and visa versa). Quantum computing is the only counterexample to this thesis. Algorithms such as factoring and finding the ground state of reasonable physics systems appear to be classically difficult but efficient on a quantum computer.

Our interest has been in determining how to leverage this additional power. We have developed and benchmarked algorithms for simulating molecules and Hubbard models on quantum computers. We have also developed new algorithms which take a Hamiltonian and generate the quantum circuit which diagonalizes it. More recently, we've been interested in developing algorithms for today's quantum devices. This includes determining algorithms which are effective on digital noisy-intermediate scale quantum computers (NISQ) as well as collaborating on analog simulation approaches to map dipolar molecular Hamiltonians (i.e. as found in Bryce Gadway's lab) to high-energy physics models.

Beyond algorithms to run on a quantum computer, we work on quantum-information related topics such as tensor networks, the entanglement of quantum circuits, Hamiltonian learning, and understanding the line between quantum and classical computing.

Algorithms for the Quantum Many Body Problem

The key to an improved understanding of the quantum many-body problem is improved algorithms. Some example successes include

*
SWO, a new machine-learning inspired approach to wave-function optimization
Neural Net Backflow, a new wave-function which solves the problem of using neural-nets with fermions by combining deep neural networks and backflow.
EHC, a new algorithm to take a wave-function and produce all the local parent Hamiltonians
VAFT, a new finite-temperature variational approach
SIMPS, a new MPS algorithm for finding interior eigenstates of a many-body MBL spectrum
combining MPS and QMC methodologies to compute many-body ground states with higher accuracy then can be computed individually
an efficient approach for using multiSlater-Jastrow in VMC.
Partial Node FCIQMC, a way to combine FCIQMC With fixed-node approaches + an understanding for how second quantization affects the sign problem.
*

I am currently teaching: **Computing in Physics ** [link]

The two courses I've developed from scratch are *Computing in Physics* and *An Algorithmic Perspective on Strongly Correlated Systems*. If you're looking for something new, check there.

Other courses I've previously taught include
Graduate Quantum Mechanics (I, II),
*Atomic Scale Simulations *,
*Undergraduate Quantum Mechanics*,
among others (see here).

Besides courses, I've given various summer school lectures (see here).

You might also be interested in learning about:

*Variational Monte Carlo:* See my notes
and video from the Boulder Summer School; the
videos [part 1, part 2] from
the Cornell Summer School on Emergent Phenomena; or my tutorials (most recently given at CECAM).

*Diffusion Monte Carlo:* See my notes
and video from the Boulder Summer School.

*Path Integral Monte Carlo: * See my tutorials (with Ken Esler and Paul Yubo).

*Density Matrix Renormalization Group: * Work through problem set 3 and problem set 4 from my graduate course to build a simple DMRG code in Julia; or
look through my simple DMRG notebook in mathematica.

* Many-Body Localization:* Handwritten lectures notes on MBL using tensor networks and frustrated magnetism from the Princeton summer school. (See here for the video)