Nav: Home

New algorithm could help find new physics

July 27, 2018

Scientists at the University of Illinois at Urbana-Champaign have developed an algorithm that could provide meaningful answers to condensed matter physicists in their searches for novel and emergent properties in materials. The algorithm, invented by physics professor Bryan Clark and his graduate student Eli Chertkov, inverts the typical mathematical process condensed matter physicists use to search for interesting physics. Their new method starts with the answer--what kinds of physical properties would be interesting to find--and works backward to the question--what class of materials would host such properties.

Inverse problem solving isn't a new technique in classical physics, but this algorithm represents one of the first successful examples of an inverse problem solving method with quantum materials. And it could make searching for interesting physics a more streamlined and deliberate process for many scientists. More physicists are working in condensed matter than any other subfield of physics--the rich diversity of condensed matter systems and phenomena provide ample unsolved problems to explore, from superconductivity and superfluidity to magnetism and topology. Experimentalists probe the macro-and microscopic properties of materials to observe the behavior and interactions of particles in materials under a strict set of controls. Theoretical condensed matter physicists, on the other hand, work to develop mathematical models that predict or explain the fundamental laws that govern these behaviors and interactions.

The field of theoretical condensed matter physics has the well-earned reputation for being esoteric and difficult for the lay person to decipher, with its focus on understanding the quantum mechanics of materials. The process of writing and solving condensed matter equations is extremely intricate and meticulous. That process generally starts with a Hamiltonian--a mathematical model that sums up the energies of all the particles in the system.

Clark explains, "For a typical condensed matter problem, you start with a model, which comes out as a Hamiltonian, then you solve it, and you end up with a wave function--and you can see the properties of that wave function and see whether there is anything interesting. This algorithm inverts that process. Now, if you know the desired type of physics you would like to study, you can represent that in a wave function, and the algorithm will generate all of the Hamiltonians--or the specific models--for which we would get that set of properties. To be more exact, the algorithm gives us Hamiltonians with that wave function as an energy eigenstate."

Clark says the algorithm gives a new way to study physical phenomena such as superconductivity.

"Typically, you would guess Hamiltonians that are likely to be superconducting and then try to solve them. What this algorithm - in theory - will allow us to do is to write down a wave function that we know superconducts and then automatically generate all of the Hamiltonians or the specific models that give that wave function as their solution. Once you have the Hamiltonians, in some sense, that gives you all the other properties of the system--the excitation spectrum, all the finite temperature properties.

That requires some more steps once you have the Hamiltonian, so we didn't improve that part of the research process. But what we did, we found a way to find interesting models, interesting Hamiltonians."

Chertkov adds, "There are lots of wave functions people have written down for which there are no known Hamiltonians--maybe 50 years worth. Now we can take any of these wave functions and ask if any Hamiltonians give those as eigenstates and you may end up with one model, no models, or many. For example, we are interested in spin-liquid wave functions, highly entangled quantum states with interesting topological properties.

Theorists have constructed many spin-liquid wave functions, but don't know which Hamiltonians give them.

In the future, our algorithm should let us find these Hamiltonians."

Clark and Chertkov tested the algorithm on wave functions related to frustrated magnetism, a topic that presents interesting physics with many open questions. Frustrated magnetism occurs in a class of materials that is insulating, so the electrons don't move around, but their spins interact. Clark explains one such wave function they tested, "The electron spins in a frustrated magnet want to be anti-aligned, like the north and south on a magnet, but can't because they live on triangles. So we make a wave function out of a linear-superposition of all of these frustrated states and we turn the crank of this algorithm, and ask, given this wavefunction, which is an interesting quantum state on a frustrated magnet, are there

Hamiltonians that would give it. And we found some."

Chertkov says the results of the algorithm could point experimentalists in the right direction to find interesting new physics: "That would hopefully be one way it would be used. You pick a wave function that has some kind of physics that you care about and you see what sort of interactions can give you that sort of physics, and hopefully then the models you find through this method can be looked for in experiments. And it turns out you find many models with our method."

Clark sums up, "This has inverted the part of the process where we were sort of hunting in the dark. Before, you could say, we're going to try lots of models until we find something interesting. Now you can say, this is the interesting thing we want, let's turn the crank on this algorithm and find a model that gives that."
-end-


University of Illinois College of Engineering

Related Algorithm Articles:

A new algorithm predicts the difficulty in fighting fire
The tool completes previous studies with new variables and could improve the ability to respond to forest fires.
New algorithm predicts optimal materials among all possible compounds
Skoltech researchers have offered a solution to the problem of searching for materials with required properties among all possible combinations of chemical elements.
New algorithm to help process biological images
Skoltech researchers have presented a new biological image processing method that accurately picks out specific biological objects in complex images.
Skoltech scientists break Google's quantum algorithm
In the near term, Google has devised new quantum enhanced algorithms that operate in the presence of realistic noise.
The most human algorithm
A team from the research group SEES:lab of the Department of Chemical Engineering of the Universitat Rovira I Virgili and ICREA has made a breakthrough with the development of a new algorithm that makes more accurate predictions and generates mathematical models that also make it possible to understand these predictions.
Algorithm turns cancer gene discovery on its head
Prediction method could help personalize cancer treatments and reveal new drug targets.
New algorithm predicts gestational diabetes
Timely prediction may help prevent the condition using nutritional and lifestyle changes.
New algorithm could mean more efficient, accurate equipment for Army
Researchers working on an Army-funded project have developed an algorithm to simulate how electromagnetic waves interact with materials in devices to create equipment more efficiently and accurately.
Universal algorithm set to boost microscopes
EPFL scientists have developed an algorithm that can determine whether a super-resolution microscope is operating at maximum resolution based on a single image.
Algorithm designed to map universe, solve mysteries
Cornell University researchers have developed an algorithm designed to visualize models of the universe in order to solve some of physics' greatest mysteries.
More Algorithm News and Algorithm Current Events

Trending Science News

Current Coronavirus (COVID-19) News

Top Science Podcasts

We have hand picked the top science podcasts of 2020.
Now Playing: TED Radio Hour

Listen Again: Meditations on Loneliness
Original broadcast date: April 24, 2020. We're a social species now living in isolation. But loneliness was a problem well before this era of social distancing. This hour, TED speakers explore how we can live and make peace with loneliness. Guests on the show include author and illustrator Jonny Sun, psychologist Susan Pinker, architect Grace Kim, and writer Suleika Jaouad.
Now Playing: Science for the People

#565 The Great Wide Indoors
We're all spending a bit more time indoors this summer than we probably figured. But did you ever stop to think about why the places we live and work as designed the way they are? And how they could be designed better? We're talking with Emily Anthes about her new book "The Great Indoors: The Surprising Science of how Buildings Shape our Behavior, Health and Happiness".
Now Playing: Radiolab

The Third. A TED Talk.
Jad gives a TED talk about his life as a journalist and how Radiolab has evolved over the years. Here's how TED described it:How do you end a story? Host of Radiolab Jad Abumrad tells how his search for an answer led him home to the mountains of Tennessee, where he met an unexpected teacher: Dolly Parton.Jad Nicholas Abumrad is a Lebanese-American radio host, composer and producer. He is the founder of the syndicated public radio program Radiolab, which is broadcast on over 600 radio stations nationwide and is downloaded more than 120 million times a year as a podcast. He also created More Perfect, a podcast that tells the stories behind the Supreme Court's most famous decisions. And most recently, Dolly Parton's America, a nine-episode podcast exploring the life and times of the iconic country music star. Abumrad has received three Peabody Awards and was named a MacArthur Fellow in 2011.