// About me

I am a postdoc at the Perimeter Institute for Theoretical Physics where I develop and apply wavefunction-based numerical methods for quantum many-body systems related to the density matrix renormalization group (DMRG). [See my notes on DMRG.]

My research concerns systems where electron interactions dominate kinetic-energy effects, in which case the electrons are said to be strongly correlated. Such materials are not well described by band theory, including most density functional approximations. Purely analytical approaches for these systems may be inconclusive or only give qualitative insights.

An exciting alternative is to combine analytics with numerics through practical and principled classes of variational wavefunctions. For example, using matrix product states in one dimension one can compute low-energy, dynamical, and finite-temperature properties of many-body systems. They also provide a framework for rigorously classifying gapped phases.

On the personal side I enjoy outdoor sports (running, skiing, golf, and paddleboarding); playing guitar and piano; and traveling.


Download my CV

// Experience

Postdoctoral Fellow — Perimeter Institute for Theoretical Physics

2013-Present


Postdoctoral Researcher — UC Irvine

Groups of Steven R. White and Kieron Burke

2010-2013
  • Discovered a method for parallelizing the density matrix renormalization group in real space.
  • Performed state-of-the-art simulations of model electronic structure systems, frustrated magnets and topologically ordered nanowires.
  • Co-developed an open source library for tensor product wavefunction algorithms. Website: http://itensor.org/.


Graduate Student Researcher — UC Santa Barbara

Advisor: Leon Balents

2005-2010
  • Applied a variety of analytical methods (bosonization, mean-field theory, spin wave calculations, high temperature series) to study frustrated magnets.
  • Developed code based on the ALPS simulation library to implement a novel semi-classical algorithm for finite temperature quantum magnets.
  • Collaborated with Steven R. White on a new method for simulating finite temperature quantum systems (the METTS algorithm).

// Education

2005-2010 Ph.D. in Physics, UC Santa Barbara. Advisor: Leon Balents
2000-2005 BS in Physics, Georgia Institute of Technology. Highest honors.
2000-2005 BS in Mathematics, Georgia Institute of Technology. Highest honors.

// Publications

2014
Lucas O. Wagner, Thomas E. Baker, E.M. Stoudenmire, Kieron Burke, and Steven R. White, "Kohn-Sham Calculations with the Exact Functional", Phys. Rev. B, 90: 045109  [Editor's suggestion]
2014
Ann Kallin, E.M. Stoudenmire, Paul Fendley, Rajiv R.P. Singh, Roger G. Melko, "Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions", J. Stat. Mech. P06009
2013
Lucas O. Wagner, E.M. Stoudenmire, Kieron Burke, and Steven R. White, "Guaranteed Convergence of the Kohn-Sham Equations", Phys. Rev. Lett. 111: 093003  [Editor's suggestion]
2013
E.M. Stoudenmire and Steven R. White, "Real-Space Parallel Density Matrix Renormalization Group", Phys. Rev. B 87: 115137
2013
Salvatore R. Manmana, E.M. Stoudenmire, Kaden R.A. Hazzard, Ana Maria Rey and Alexey Gorshkov, "Topological phases in polar-molecule quantum magnets", Phys. Rev. B 87: 081106(R)
2012
E.M. Stoudenmire, Lucas O. Wagner, Steven R. White and Kieron Burke, "One-dimensional continuum electronic structure with the density matrix renormalization group and its implications for density functional theory",
Phys. Rev. Lett. 109: 056402
2012
Lucas O. Wagner, E.M. Stoudenmire, Steven R. White and Kieron Burke, "Reference electronic structure calculations in one dimension",
Phys. Chem. Chem. Phys. 14: 8581
2012
E.M. Stoudenmire and Steven R. White, "Studying two-dimensional systems with the density matrix renormalization group", Annual Reviews of Condensed Matter Physics 3: 111
2011
E.M. Stoudenmire, Jason Alicea, Oleg A. Starykh and Matthew P.A. Fisher, "Interaction effects in topological superconducting wires supporting majorana fermions", Phys. Rev. B 84: 014503  [Editor's suggestion, Synopsis Article]
2010
E.M. Stoudenmire and Steven R. White, "Minimally entangled typical thermal state algorithms", New J. Phys. 12: 055026
2009
E.M. Stoudenmire, Simon Trebst and Leon Balents, "Quadrupolar correlations and spin freezing in S=1 triangular lattice antiferromagnets",
Phys. Rev. B 79: 214436
2008
E.M. Stoudenmire and Leon Balents, "Ordered phases of the anisotropic kagome lattice antiferromagnet in a field", Phys. Rev. B 77: 174414
2005
E.M. Stoudenmire and C.A.R. Sá de Melo, "Magnetoresistive effects in ferromagnet-superconductor multilayers" J. Appl. Phys. 97: 10J108

Minimally Entangled Typical Thermal States (METTS)

What does a snapshot of a thermal quantum state look like?

Quantum Monte Carlo methods have been very successful in simulating thermal quantum systems by mapping them to classical ensembles which can be efficiently sampled. However, this approach can fail dramatically for systems with mobile fermions or frustrated magnetic exchange interactions, in which case the system is said to have a "sign problem".

One way around the sign problem is to represent a thermal quantum system as an ensemble of pure-state wavefunctions instead of virtual classical states. A particularly efficient ensemble to sample is the set of minimally entangled typical thermal states or METTS. These states are descendants of classical product wavefunctions which contain just enough entanglement to capture finite-temperature quantum correlations.

METTS not only provide an efficient method for simulating thermal quantum systems in 1d and 2d, but provide an intuitive picture of thermal quantum states. There is a wealth of systems waiting to be studied with METTS including one- and two-dimensional frustrated spin-lattice models and continuum electronic wires. We are also investigating powerful new extensions to the basic METTS algorithm that will enable us to push further into two dimensions.

More Reading:

  • Steven R. White, "Minimally entangled typical quantum states at finite temperature", Phys. Rev. Lett. 102: 190601 (2009)
  • E.M. Stoudenmire and Steven R. White, "Minimally entangled typical thermal state algorithms", New J. Phys. 12: 055026 (2010)

Exact Density Functional Theory With Model 1D Systems

At the heart of the enormously successful density functional theory (DFT) method lies a functional that gives the ground state energy of any system provided only its density. Can this exact energy functional be written down? What are its key properties?

Except for a handful of small systems, computing the exact functional in three dimensions is too difficult to allow a systematic study of its properties. However, in one dimension the extreme power of the density matrix renormalization group (DMRG) allows us to calculate the exact densities of a wide variety of continuum, long-range interacting systems resembling long chains of artificial atoms. From these exact densities, it is relatively straightforward to calculate the exact density functional and a host of other quantities of interest in DFT. We can then use our 1d laboratory to study established density-functional approximations and explore improved functionals which could be applied to strongly correlated systems in 3d.

I gave a talk on this subject in November 2012 at the Perimeter Institute, and a slightly more pedagogical talk at National Taiwan University in December 2012.

Related works:

  • Lucas O. Wagner, Thomas E. Baker, E.M. Stoudenmire, Kieron Burke, and Steven R. White, "Kohn-Sham Calculations with the Exact Functional", arxiv:1405.0864
  • Lucas O. Wagner, E.M. Stoudenmire, Kieron Burke, and Steven R. White, "Guaranteed convergence of the Kohn-Sham equations", Phys. Rev. Lett. 111: 093003 (2013)
  • E.M. Stoudenmire, Lucas O. Wagner, Steven R. White and Kieron Burke, "One-dimensional continuum electronic structure with the density matrix renormalization group and its implications for density functional theory", Phys. Rev. Lett. 109: 056402 (2012)
  • Lucas O. Wagner, E.M. Stoudenmire, Steven R. White and Kieron Burke, "Reference electronic structure calculations in one dimension", Phys. Chem. Chem. Phys. 14: 8581 (2012)

The Intelligent Tensor (ITensor) C++ Library

What does a DMRG wavefunction look like?

Beginning with the work of Östlund and Rommer, it has become clear that the density matrix renormalization group (DMRG) is just one of a family of powerful methods for simulating quantum systems. The concept linking these methods is the tensor network state, a diagrammatic language for capturing the internal structure of many-body wavefunctions.

The ITensor Library is an open source C++ library for rapidly developing and applying tensor network algorithms. ITensor is competitive with publicly available codes when performing straight DMRG calculations, but its flexibility has enabled us to extend DMRG in ways that would be inconceivable with other approaches. It is especially well suited for developing next-generation tensor network algorithms such as PEPS, MERA, and METTS (see above).

See a list of papers written using ITensor.

// Contact



E.M. Stoudenmire
Perimeter Institute for Theoretical Physics
31 Caroline St N
Waterloo, Ontario, Canada
N2L 2Y5