# Quantum Phase Transitions

### Quantum Antiferromagnetism in Chromium

The only elemental antiferromagnet, Cr, has spin-density-wave and charge-density-wave transitions that can be suppressed smoothly to T = 0 by doping with V or by applying pressure. Both the pure and doped systems are sufficiently simple in composition to offer the hope of theoretical tractability. Combining high-resolution magnetotransport and synchrotron x-ray measurements on pure Cr under pressure provides a unique opportunity to study the behavior of strongly-interacting, magnetically-modulated itinerant fermions in the immediate vicinity of an approachable quantum critical point. We are particularly interested in the breakdown of the BCS ground state and its relation to the onset of superconductivity in the rare earth cuprates. Comparisons between pure Cr and Cr1-xVx crystals provide insight into the role played by disorder.

More reading:

"Breakdown of the Bardeenâ€“Cooperâ€“Schrieffer ground state at a quantum phase transition"

"Signatures of quantum criticality in pure Cr at high pressure"

"Direct probe of Fermi surface evolution across a pressure-induced quantum phase transition"

### Dimensionality and Symmetry

Dimensionality and symmetry play deterministic roles in the laws of Nature. They are important tools to characterize and understand quantum phase transitions, especially in the limit of strong correlations between spin, orbit, charge, and structural degrees of freedom. Here, using newly-developed, high-pressure resonant X-ray magnetic and charge diffraction techniques, we have discovered a quantum critical point in Cd_{2}Os_{2}O_{7} as the all-in-all-out antiferromagnetic order is continuously suppressed to zero temperature and, concomitantly, the cubic lattice structure continuously changes from space group Fd-3m to F-43m. Sur- rounded by three phases of different time reversal and spatial inversion symmetries, the quantum critical region anchors two phase lines of opposite curvature, with striking depar- tures from a mean-field form at high pressure. As spin fluctuations, lattice breathing modes, and quasiparticle excitations interact in the quantum critical region, we argue that they present the necessary components for strongly-coupled quantum criticality in this three- dimensional compound.

More reading: Strongly-coupled quantum critical point in an all-in-all-out antiferromagnet

### Competing Ground States

Pure CeFe_{2} has a ferromagnetic ground state that coexists with strong antiferromagnetic spin fluctuations, as well as an electron system that is intermediate between itinerant and localized. It is highly susceptible to pressure, and high-energy magnetic x-ray diffraction at low temperature for crystals compressed inside a diamond anvil cell provides direct information on a quantum phase transition between ferromagnetism and antiferromagnetism. The behavior of CeF_{2} at its quantum critical point is of interest in its own right, and additionally may be relevant to the behavior of a recently discovered class of Ce-based heavy fermion superconductors.

More reading: "Pressure tuning of competing magnetic interactions in intermetallic CeFe_{2}"

### Shastry-Sutherland Quantum Antiferromagnetism

The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional square lattice, is simple and soluble, but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu_{2}(BO_{3})_{2}, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state.

More reading:

Continuous and discontinuous quantum phase transitions in a model two-dimensional magnet

Emergence of long-range order in sheets of magnetic dimers

Crystallization of spin superlattices with pressure and field in the layered magnet SrCu_{2}(BO_{3})_{2}

### The Metal-Insulator Transition in the Strongly Correlated Limit

The transition metal chalcogenide, NiS_{2}, is one of the select few Mott-Hubbard materials without a strong structural instability tied to the localization of charge. We are elucidating the quantum critical behavior with an emphasis on deconvoluting the roles played by the antiferromagnetism (present on both sides of the metal-insulator transition), by the disorder, and by the dynamical response.

More reading: Magnetism, structure, and charge correlation at a pressure-induced Mott-Hubbard insulator-metal transition