Quantum critical point | EPFL Graph Search

A quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero. A quantum critical point is typically achieved by a continuous suppression of a nonzero temperature phase transition to zero temperature by the application of a pressure, field, or through doping. Conventional phase transitions occur at nonzero temperature when the growth of random thermal fluctuations leads to a change in the physical state of a system. Condensed matter physics research over the past few decades has revealed a new class of phase transitions called quantum phase transitions which take place at absolute zero. In the absence of the thermal fluctuations which trigger conventional phase transitions, quantum phase transitions are driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle. Overview Within the class of phase transitions, there are two main categories: at a first-order phase t

Single Crystal Growth of Constantan by Vertical Bridgman Method

This project deals with aspects involved in the growth of single-crystals of Constantan. Constantan is an alloy of Nickel in Copper, whose technological interest is that resistance is independent of temperature over a very large range of temperatures (hence the name Constantan). This, along with other suitable properties such as high strain sensitivity, high resistivity and low coefficient of thermal expansion makes it the principal component of all modern strain gauges used. However, Constantan also represents exactly the critical composition of Nickel in Copper (45% by weight Ni in Cu), which is the border between ferromagnetism and paramagnetism at low temperature. Such a transition in magnetic states at low (zero) temperature is called a quantum phase transition, and results in a uniquely scaling excitation spectrum. The eventual purpose of growing these single crystals is to validate our hypothesis that in fact the technologically relevant properties of Constantan are the result of quantum critical fluctuations. This can be investigated by a technique called inelastic neutron scattering.

2011

Probing Entangled States of the Nuclear-Electronic Quantum Magnet LiHoF₄

Ivan Kovacevic

Two objects are entangled when their quantum mechanical wavefunctions cannot be written in a separable product form. Entangling dissimilar quantum objects, or hybridization, has been suggested as a promising route to efficient quantum information processors, but mostly realized on a limited scale. Hybrid nuclear-electronic many-body systems remain a largely unexplored challenge to both experiments and theories. The prototypical transverse-field Ising ferromagnet LiHoF4 is an ideal platform to address this issue. The Ising model is considered as an archetype both for the investigation of quantum criticality and for the evaluation of quantum simulators. The hyperfine coupling strength of a Ho ion is exceptionally large, promoting a strong hybridization or entanglement between the nuclear and electronic moments. The magnetic coupling between the Ho ions that leads to ferromagnetic ordering is predominantly through long-range dipole interactions, while nearest-neighbor exchange interaction is negligibly weak. Applying a transverse field induces a zero temperature quantum phase transition driven by quantum fluctuations. Altogether LiHoF4 represents a unique nuclear-electronic quantum magnet, whose wavefunctions can be readily obtained by diagonalizing the Hamiltonian using the mean-field approximation. In this thesis we develop an experimental setup to probe the entangled nuclear-electronic states in a model transverse-field Ising system LiHoF4. Using magnetic resonance the field and temperature evolution of the nuclear-electronic states are successfully traced across the whole phase diagram. We develop a theoretical framework based on mean-field calculations which provides close agreement with the experimental observations. Having established experimentally that the mean-field wavefunctions are an excellent approximation of the actual wavefunction, we used them to calculate the ground-state entanglement entropy between the electronic and nuclear magnetic moments. We find that the entanglement entropy between the nuclear and electronic moments exhibits a peak at the quantum phase transition. This suggests that the electronic entanglement is encoded onto each nuclear-electronic state. Our results pave the way for new theoretical and experimental investigations of quantum entanglement.

EPFL2016

Simulated annealing study of the disordered quantum magnet LiHoxEryY1-x-yF4

Thermal and quantum phase transitions of some rare earth compounds (LiErF4, LiYbF4, LiGdF4 and LiTmF4) are established using the mean field theory. These preliminary calculations allowed evidencing the existence of a novel high-field antiferromagnetic phase in LiErF4, and a still unexplained symmetry breaking in LiGdF4. But the discrepancies with experimental results impel a more sophisticated method. We then present analytical and numerical evidence for the validity of an effective approach to the description of the dipolar coupled antiferromagnet LiErF4. We show that the approach, when implemented in mean field calculations, is able to capture both the qualitative and quantitative aspects of the physics of LiErF4 at small external field and low temperature, yielding results that agree with those obtained in the full Hilbert space using mean field theory. This model nevertheless still fails to describe the LiHoF4 system and needs to be improved. We finally use this toy model as a basis for classical Monte Carlo simulations of LiErF4, which allows the calculation of thermodynamical quantities of the system, as well as the evolution of the order parameters as a function of field H and temperature T. These calculations yield results that are much closer to the experiments than those based on the mean field approximation. Although the theoretical critical temperature is still overestimated by 34%, the critical exponents computed from this effective model correspond to those found experimentally.

2012