Quantum phase transition discovered in a quasi-2D system consisting only of spins

Pure quantum systems can undergo phase transitions analogous to the classical phase transition between the liquid and gaseous states of water. At the quantum level, however, the particle rotates in states that emerge from phase transitions displaying collective entangled behavior. This unexpected observation offers a new avenue for the production of materials with topological properties useful in applications of spintronics and quantum computing.

The discovery was made by an international collaboration led by Julio Larrea, professor at the Institute of Physics at the University of São Paulo (IF-USP) in Brazil. Larrea is the first author of an article on the study published in Nature.

“We obtained the first experimental evidence of a first-order quantum phase transition in a quasi-two-dimensional system composed entirely of spins. It was a revolutionary study in terms of experimental development and theoretical interpretation,” said Larrea.

To understand the importance of this discovery, it will be useful to examine the classical phase transition, which can be illustrated by the change of state of water, and its quantum analogue, illustrated by the Mott metal-insulator transition. .

“The change in state of water, which occurs at 100 ° C under normal atmospheric pressure, is called a first order transition. It is characterized by a discontinuous jump in molecular density. In other words, the number of water molecules per unit volume varies greatly from state to state, ”said Larrea. “This first-order discontinuous transition evolves with pressure and temperature until it is completely suppressed at the so-called critical water point, which occurs at 374 ° C and 221 bar. At the critical point. , the transition is of the second order, that is to say continuous. “

Near the critical point, the properties of water behave abnormally, because density fluctuations are infinitely correlated on the atomic length scale. As a result, the material manifests a unique state that differs from both a gas and a liquid (see Figure 1).

“In quantum matter, the metal-to-insulator Mott transition is a rare example of a first-order transition. Unlike ordinary metals and insulators, which have free electrons that do not interact, a Mott state involves a strong interaction. between electronic charges, collectively configuring behavior, ”explained Larrea.“ The energy scales of these interactions are very small, so a first-order quantum phase transition between a metal and an insulator can occur at absolute zero, which is the lowest possible temperature. The interaction between the charges varies with temperature and pressure until it is removed at the critical point. As the critical point approaches, the volume charge density, which is the amount of charge per unit volume, undergoes a change so abrupt that it can induce new states of matter such as superconductivity.

In the two examples cited, the phenomena involve massive particles such as water molecules and electrons. The question posed by the researchers was whether the concept of phase transition could be extended to massless quantum systems, such as a system composed only of spins (understood as a quantum manifestation of matter associated with magnetic states). A situation like this had never been observed before.

“The material we used was a frustrated quantum antiferromagnetic SrCu₂(BO₃)₂“said Larrea.” We measured the specific heat of small samples under extreme temperature conditions simultaneously [to 0.1 kelvin], pressure [to 27 kilobar] and magnetic field [to 9 tesla]. Specific heat is a physical property that gives us a measure of the internal energy in the system, and from there we can deduce different types of ordered or disordered quantum states, and possible electronic or spin states. entangled. “

Obtaining these measurements with the precision required to reveal correlated quantum states, using samples subjected to extremely low temperatures, high pressures and strong magnetic fields, was a formidable experimental challenge, according to Larrea. The experiments were carried out in Lausanne, Switzerland, at the Quantum Magnetism Laboratory of the Federal Polytechnic of Lausanne (LQM-EPFL), headed by Henrik Rønnow. The precision of the measurements motivated the theoretical collaborators, led by Frédéric Mila (EPFL) and Philippe Corboz (University of Amsterdam), to develop cutting-edge calculation methods making it possible to interpret the various anomalies observed.

“Our results showed unexpected manifestations of quantum phase transitions in pure spin systems,” said Larrea. “First, we observed a quantum phase transition between two different types of entangled spin state, the dimer state [spins correlated at two atomic sites] and the wafer state [spins correlated at four atomic sites]. This first-order transition ends at the critical point, at a temperature of 3.3 Kelvin and a pressure of 20 kilobar. Although the critical points of water and the SrCu₂(BO₃)₂ spin system have similar characteristics, states that emerge near the critical point of the spin system conform to a different description of physics, of the Ising type. The term Ising refers to a model of statistical mechanics named after the German physicist Ernst Ising (1900 -98).

“We have also observed that this critical point presents a discontinuity in the density of magnetic particles, with triplets or correlated states in different configurations of spin orientation, leading to the emergence of a purely quantum antiferromagnetic state”, a declared Larrea (see figure 2).

The next step for Larrea is to learn more about the criticality and entangled spin states that emerge near the critical point, the nature of discontinuous and continuous quantum phase transitions, and the energy scales that represent interactions and correlations between spins and charges leading to quantum states such as superconductivity. “To this end, we plan to conduct a study with pressures around the critical point and higher pressures,” he said. A new facility, the Laboratory of Quantum Matter in Extreme Conditions (LQMEC), is being set up for this purpose in collaboration with Valentina Martelli, professor in the Department of Experimental Physics at IF-USP.