Robust Computational Model for New State of Matter – Strange Metals

Using cutting-edge computational techniques, researchers from the Flatiron Institute in New York City and Cornell University have solved the first robust theoretical model of strange metals. The work reveals that strange metals are a new state of matter.

Strange metals share remarkable properties with black holes, opening exciting new directions for theoretical physics.

In a strange metal, electrical conductivity is linked directly to temperature and to two fundamental constants of the universe: Planck’s constant and Boltzmann’s constant. Strange metals are also known as Planckian metals.

Models of strange metals have existed for decades, but accurately solving such models proved out of reach with existing methods. Quantum entanglements between electrons mean that physicists can’t treat the electrons individually, and the sheer number of particles in a material made the calculations more difficult to solve.

Cha and his colleagues used two different methods to crack the problem.

1. they used a quantum embedding method based on ideas developed by Georges in the early ’90s. With this method, instead of performing detailed computations across the whole quantum system, physicists perform detailed calculations on only a few atoms and treat the rest of the system more simply.

2. They used a quantum Monte Carlo algorithm (named for the Mediterranean casino), which uses random sampling to compute the answer to a problem.

Strange metals are a new state of matter bordering two previously known phases of matter: Mott insulating spin glasses and Fermi liquids. There is a whole region in the phase space that has Planckian behavior and are not spin glasses or Fermi liquids. Strange metals are a sluggish, soupy, slushy state.

The advances here will help understand the physics of higher-temperature superconductors and the physics of black holes.

PNAS – Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions

In “Planckian metals,” electrons dissipate energy at the fastest possible rate allowed by the fundamental laws of quantum mechanics, resulting in a linear temperature dependence of their electrical resistivity. Although observed for a number of quantum materials, this phenomenon lacks a general theoretical understanding and is often considered as one of the prominent fundamental questions in condensed matter physics. Here, we show that Planckian dissipation and a behavior consistent with the “marginal Fermi liquid” phenomenology emerge in the quantum critical regime separating a Mott insulating spin glass and a Fermi liquid. By establishing this behavior in an explicit model solvable by state-of-the-art computational methods, our theory paves the way toward a deeper understanding of Planckian or “strange” metals.

“Strange metals” with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-1/2 fermions interacting via onsite Hubbard interaction and random infinite-ranged spin–spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of SU(M) symmetric models to models with physical SU(2) spin-1/2 electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

SOURCES – Proceedings of the National Academy of Sciences.
Written By Brian Wang,