Physicists elucidate connection between symmetry and Mott physics

Superconductivity has provided physicists with many theoretical challenges and experimental surprises. Superconductivity has been in the spotlight for its scientific importance and potential applications since 1957, when the Bardeen-Cooper-Schrieffer (BCS) theory was developed at the University of Illinois.

High-temperature superconductivity is one of the biggest problems in physics. Illinois has a strong tradition of breakthrough discoveries in this field, and physicists have recently discovered a connection between symmetry and the physics underlying high-temperature superconductors. These theoretical findings were published in the journal Nature Physics.

From broken symmetries to Fermi liquids.

The record for the highest transition temperature at ambient pressure is held by the cuprates. The electrons in these materials are interacting in a way that is different from normal metals. Strong interactions can be dealt with by focusing on models such as the Hubbard model. The models have inherent complexity and must be simulations. Illinois researchers have found a description that explains the physics in beautiful detail.

The problem of superconductivity is not easy to solve. We found a way around it. A simplified symmetry allows us to think about interactions in a new way.

In 2001 Philip Anderson and Duncan Haldane discovered a symmetry by writing down a particle-hole transformation that preserves the Hamiltonian of a Fermi liquid.

The standard theory of metals contains a hidden symmetry, one that is associated with interchanging particles and holes for just a single spin species.

ott insulators are often thought of as things that don't break. They don't break any symmetries in this view, so it's difficult to describe them. The hidden symmetry pointed out by Anderson and Haldane was broken by them.

This is a crucial step. The key insight the researchers made in the current work is that if you break this symmetry by adding or removing particles or holes, you will destroy a Fermi liquid. This observation implies that all models of Mott insulators must break this symmetry.

There is a fixed point.

A theory of superconductivity was developed by John Bardeen and his team to solve superconductivity in normal metals. The goal for the team was to develop a theory for high-temperature superconductivity by starting with a Mott insulator.

To solve the high-temperature superconductivity problem, one must do exactly what Bardeen did. One needs to show that there is a fixed point and that only superconductivity can destroy it.

The researchers looked at models that broke the hidden symmetry of the Fermi liquid and might lead to fixed points.

The result is a surprise, after we asked what the simplest model that breaks this symmetry was. The Hatsugai-Kohmoto model was proposed in 1992 but no one took it seriously.

The Hubbard model has been the most popular way of tackling high-temperature superconductivity. It is difficult to get rigorous results for this model. The one-dimensional case shows that the Hubbard model is solvable.

The simplicity of the Hatsugai-Kohmoto model is appealing. The HK model was shown to have non-BCS superconductivity after the team provided an exact solution.

The simplest model that breaks the particle-hole symmetry is the HK model. The researchers tracked the symmetries that survived the transition. They found that the HK model breaks the same hidden symmetry as Anderson and Haldane in Fermi liquids. They showed that the HK model introduces the correct and relevant action for Mott insulation. The broken symmetry shows that a new fixed point is a critical piece of the puzzle for solving the high-temperature superconductivity problem.

A system of non-Interacting particles and repulsive short-range interactions can be used to illustrate a fixed point. Upon introducing such interactions, one recovers a Fermi liquid. That is, a Fermi liquid is stable in state space.

One way to escape the liquid fixed point is to allow electrons to interact with each other pairwise.

Another way to escape is through symmetry breaking.

The Hubbard model breaks the particle-hole symmetry. The HK model shows the generality of the Hubbard model.

The HK model is a general way of understanding how one breaks a Fermi liquid with a hidden symmetry that was pointed out in 2001. The fixed point puts us in a completely different regime of phase space from Fermi liquids.

The overreliance that theorists have had on models such as the Hubbard model has been alleviated by this result. The HK model is able to explain high-temperature superconductivity in broad generality. The Hubbard and HK models are both in the same universality class, which is a goal of statistical mechanics and renormalization group theory.

The answer to the particle-hole asymmetry problem is finally here.

Anderson pointed out the failure of the physics community to address particle-hole symmetry breaking in strongly correlated systems.

Anderson wrote "I remain baffled by the almost universal refusal of theorists to confront this evident fact of hole-particle asymmetry head-on."

The HK model breaking the symmetry leads to the basis of high-temperature superconductivity, which is why the team is optimistic that their work will serve as a controlled platform.

Physicists thought that the only way to get physics was to solve the Hubbard model, but they didn't need a model at all. The HK model was viewed as a curiosity by many. They didn't know that it created a fixed point or that it broke a symmetry. They didn't know that this model leads to the violation of Fermi liquid theory. We did not follow up on this symmetry until we did.

The hurdle was holding everyone back. People would have solved the HK model long ago if they had realized that there are two different classes of superconductors. That is what we did.

More information: Edwin W. Huang et al, Discrete symmetry breaking defines the Mott quartic fixed point, Nature Physics (2022). DOI: 10.1038/s41567-022-01529-8 Journal information: Nature Physics Citation: Physicists elucidate connection between symmetry and Mott physics (2022, March 22) retrieved 22 March 2022 from https://phys.org/news/2022-03-physicists-elucidate-symmetry-mott-physics.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.