Synopsis: Fractals and quantum criticality

Theorists show that the quantum critical states of fermions may have fractal character and predict signatures of this result in liquid 3He, a fermionic fluid.
Synopsis figure

Unlike classical transitions, which involve thermal fluctuations, quantum phase transitions are driven solely by quantum fluctuations and occur when a parameter, such as density or magnetic field, is varied at zero temperature. Signatures of this zero-temperature transition—quantum critical behavior—can be seen even at finite temperature.

While it is possible to describe quantum critical states of bosons using Monte Carlo methods, a similar approach for fermions is a major challenge. The reason is the famous minus sign that appears in front of the wave function for fermions when the fermions are interchanged. As a result, the amplitudes of these wave functions cannot be interpreted as probabilities—a problem that worsens with decreasing temperature.

Writing in Physical Review B, Frank Kruger and Jan Zaanen of the University of Leiden in the Netherlands address the physics of fermionic quantum criticality by applying a path-integral formalism that encodes fermionic statistics as a geometric constraint on a bosonic system. How does a bosonic system store information about the Fermi energy—a quantity that applies uniquely to fermions? The geometric constraint takes the form of a nodal hypersurface that confines particles to pockets whose size is related to the Fermi energy. At a zero-temperature critical point, the size of these pockets vanishes, which, for instance, makes the quasiparticles in a heavy-fermion system infinitely massive, and gives rise to scale invariance—a signature of fractal behavior—of the nodal surface.

The authors show how this fractal behavior would influence the thermodynamic response functions of liquid 3He, a fermionic fluid. The results could potentially be applied to understanding quantum critical behavior in heavy-fermion metals and high-temperature superconductors. - Sarma Kancharla


Features

More Features »

Announcements

More Announcements »

Subject Areas

Quantum Physics

Previous Synopsis

Next Synopsis

Biological Physics

Polarization in hot water

Read More »

Related Articles

Synopsis: Putting the Squeeze on Magnetic Resonance
Magnetism

Synopsis: Putting the Squeeze on Magnetic Resonance

Electron-spin-resonance measurements can achieve greater sensitivity using squeezed light as an input. Read More »

Synopsis: Direct View of Exchange Symmetry
Quantum Physics

Synopsis: Direct View of Exchange Symmetry

A proposed set of experiments could offer a direct measurement of the fundamental quantum property that distinguishes fermions from bosons. Read More »

Viewpoint: Squeezed Environment Boosts Engine Performance
Nanophysics

Viewpoint: Squeezed Environment Boosts Engine Performance

A tiny engine can surpass the Carnot limit of efficiency when researchers engineer the thermal properties of the environment. Read More »

More Articles