Our group connects the microscopic degrees of freedom which make up the "rules" of our universe to the emergent phenomena which arises from them. These degrees of freedom are inherently quantum-mechanical and can include the electrons in a material, spins in a lattice model, or gates in a quantum computation.
The emergent behavior is a priori unexpected from its individual aspects; a holistic effect that is both more and different from the sum of its parts. They span many of the deepest problems in science: high temperature superconductivity, heavy fermions, quantum hall, spin liquids, topological phases, and many effects in ab-initio materials. In addition to their theoretical interest, progress in emergent phenomena promises to have important practical applications ranging from designing materials with higher superconducting temperatures to making topological quantum computing possible. Our research encompasses various areas of many-body physics including condensed matter, AMO, and quantum computing.
The tools our group uses are primarily numerical including quantum Monte Carlo, tensor networks, and various methods inspired by quantum information. We not only apply but develop new algorithms to broaden the horizon of accessible many-body systems.
Congratulations to Xiongjie Yu for graduating! We wish him luck in his new position at Akuna Capital.October 15, 2017
We have recently posted our work Exploring one particle orbitals in large Many-Body Localized systems. This is a really comprehensive examination of the MBL eigenstates beneath the mobility edge. One of the more exciting things we found was evidence that eigenstates under the mobility edge are aware of the ergodic phase for their Hamiltonian at higher energy density.September 21, 2017
Congratulations to Dmitrii for passing his prelim!August 15, 2017
This semester I'm developing and teaching a new course: Computing in Physics.July 17, 2017
I'll be talking at the Stochastic Methods in Electronic Structure Theory Conference in Telluride. Please stop by and talk if you're around!July 11, 2017
I'll be giving a summer school tutorial (as well as some lectures) on Path Integral Monte Carlo at the Telluride School on Stochastic Approaches to Electronic Structure Calculations.July 3, 2017
I'll be giving a talk on new finite temperature methods at the Workshop on Understanding Quantum Phenomena with Path Integrals If you're around, please come chat.June 2017
'Ask the scientist' is done for the semester.June 1, 2017
Congratulations to Eli for getting a 2017 NSF Grad Fellowship Honorable Mention as well as one of the Scott Anderson Outstanding Graduate Assistant Awards for 2017 from our department. Congratulations to Dmitrii for winning the departments 2017 Jordan Asketh Award, which recognizes one of the year’s outstanding European graduate students.May 30, 2017
I've just finished teaching graduate quantum mechanics II. Favorite topics: Path Integrals and quantum many-body physics.May 8, 2017
Our paper, Finite temperature properties of strongly correlated systems via variational Monte Carlo has now come out in PRB.April 5, 2017
I recently wrote a physics viewpoint on Hai-Jun Liao, et. al work on the KAHF spin liquid.March, 14 2017
Our paper The mother of all states of the kagome quantum antiferromagnet has been posted. In it, we report the existence of a new analytically solvable macroscopically degenerate point on the kagome lattice (called XXZ0), mapped out the phase diagram for how XXZ0 connects to the KAHF spin liquid, and argue that the KAHF spin liquid is actually a critical point!March 1, 2017
Come find us at the March Meeting! I'll be giving a talk on efficient algorithms for finding unitary matrix-product operators. My students/postdocs are giving talks on our work on stuffed honeycomb (Dmitrii), our work on a new macroscopically degenerate point in the kagome (Hitesh), our new finite temperature algorithm (Jahan), our new inverse QMC technique (Eli) and looking at MBL use the one-body density matrix (Benjamin).January 10, 2017
Our paper Encoding the structure of many-body localization with matrix product operators has finally been published!January 3, 2017
Our paper Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians has been published in PRL. It's on two new algorithms for finding eigenstates of many-body localized phases.
Statistical mechanics tells us that in a closed quantum system, the larger system should act as a heat bath for a small subsystem. The system is "ergodic." In quantum systems with interactions and sufficiently strong disorder, the system can enter a phase of matter - the many-body localized (MBL) phase - where ergodicity breaks down. This phenomena can exist out to infinite temperature and is a rare example of quantum mechanics dominating the qualitative physics at high temperatures.
One recent interest of our group has been using tensor networks as both a conceptual language as well as a numerical tool to understand the many-body localized phase.
In addition to working with tensor networks, we've recently discovered bimodal behavior of the entanglement entropy in the critical regime of the MBL transition both within and between disordered samples. We have also developed a new observable to examine MBL with (the cut-averaged entanglement entropy) which has the property that it is smooth even for a single disorder realization!
In another project, we explored the MBL phase analytically and numerically in infinite dimension using a wave-function approach inspired by the random energy model.
(Ferro)-magnetism was known even by 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 various exotic phenomena can arise. The prototypical way to frustrate anti-ferromagnetic spins in the Ising limit is by placing them on triangles pasted together in some way (such as in the kagome lattice on a corner sharing lattice).
Most recently, we have shown variational evidence for the existence of a chiral spin liquid in a square hopping model with pi-flux per plaquette as well as given strong numerical evidence for a chiral spin liquid in the 2/3 magnetic plateau of the kagome lattice at the XY point.
To learn more about frustrated magnetism, see my talk at the Perimeter Institute on variational methods applied to the honeycomb and kagome lattice.
In experimental physics, the design of a new apparatus has been the source of many important breakthoughs. Similarly, important results in theoretical physics are driven by new computational algorithms. Our group develops new algorithms to tackle the quantum many-body problem both improving accuracy and computational complexity. Examples of success' include
The extended Church-Turing thesis states that anything that can be computed quickly, can also be computed quickly on a Turing machine (or your Macbook). Quantum computing is the first real challenge to this thesis. Algorithms such as factoring and finding ground states of reasonable physical systems appear to be classically difficult but possible on a quantum computer. Recently, we've been thinking about whether this additional power is only of theoretical interest or can realistically be leveraged in our lifetime (for example, in quantum chemistry or lattice models). We're also interested in questions related to topological quantum computing and the interplay between quantum information and tensor networks.
I am currently teaching: Computing in Physics [link]
The two courses I've developed are Computing in Physics and An Algorithmic Perspective on Strongly Correlated Systems. If you're looking for something new, check there.
Besides courses, I've given various summer school lectures (see here). Summer school lectures (especially chalk talks) don't always translate online well, but here are some of the more useful artifacts from them: