Avalanches and universality in condensed matter

Rémi Jullien, Luca Peliti, R. Rammal +1 more

Valdir C. Aguilera-Navarro

Ann B. Kallin

At the interface of quantum information and condensed matter physics, the study of entanglement in quantum many-body systems requires a new toolset which combines concepts from each. This thesis introduces a set of computational methods to study phases and phase transitions in lattice models of quantum systems, using the Renyi entropies as a means of quantifying entanglement. The scaling of entanglement entropy can give valuable insight into the phase of a condensed matter system. It can be used to detect exotic types of phases, to pinpoint transitions between phases, and can give us universal information about a system. \nThe first approach in this thesis is a technique to measure entanglement in finite size \nlattice systems using zero-temperature quantum Monte Carlo simulations. The algorithm \nis developed, implemented, and used to explore anomalous entanglement scaling terms in \nthe spin-1/2 Heisenberg antiferromagnet. \nIn the second part of this thesis, a new and complementary numerical technique is introduced to study entanglement not just in finite size systems, but as we approach the thermodynamic limit. This “numerical linked-cluster expansion” is used to study two different systems at their quantum critical points — continuous phase transitions occurring at zero temperature, at which these systems exhibit universal properties. Remarkably, these universal properties can be reflected in the scaling of entanglement. \nEntanglement offers a new perspective on condensed matter systems, one which takes us closer to genuinely understanding what goes on in these materials at the quantum mechanical level. This thesis demonstrates the first steps in developing an extensive list of computational tools that can be used to study entanglement over a wide range of interacting quantum many-body systems. With the ever increasing computational power available, it may be only a matter of time before these tools are used to create a comprehensive framework for the characterization of condensed matter phases and phase transitions.

A. R. Bishop

Alessio Celi, Anna Sanpera, V. Ahufinger +1 more

Abstract The year 2015 was the International Year of Light. However, it also marked, the 20th anniversary of the first observation of Bose–Einstein condensation in atomic vapors by Eric Cornell, Carl Wieman and Wolfgang Ketterle. This discovery could be considered as one of the greatest achievements of quantum optics that has triggered an avalanche of further seminal discoveries and achievements. For this reason we devote this essay for the focus issue on ‘Quantum Optics in the International Year of Light’ to the recent revolutionary developments in quantum optics at the frontiers of all physics: atomic physics, molecular physics, condensed matter physics, high energy physics and quantum information science. We follow here the lines of the introduction to our book ‘Ultracold atoms in optical lattices: Simulating quantum many-body systems’ (Lewenstein et al 2012 Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford: University Press)), and to a lesser extent the review article M Lewenstein et al (2007 Adv. Phys. 56 243 ). The book, however, was published in 2012, and many things has happened since then—the present essay is therefore upgraded to include the latest developments.

William P. Reinhardt, Perry, Heidi

The possibility, envisaged in 1925 by Einstein following the suggestion of Bose, of a dilute gas of atoms being condensed into a single quantum state was experimentally achieved in 1995 following decades of research. An avalanche of experiment and theory has followed, leading to the awarding of the 2001 Nobel Prizes in Physics to three of the pioneering experimentalists. Theory, mostly couched in the language and formalism of condensed matter physics, has developed apace. What we point out here is that a condensate in a double well trap may be thought of exactly as a diatomic molecule with delocalized molecular orbitals (MOs) filled with Bosons, rather than electrons. As in quantum chemistry, configuration interaction must be included to supplement the MO picture if dissociation is to be correctly described. Such dissociation is called condensate fragmentation in the condensed matter theory literature. Natural orbitals and their occupation numbers provide a clear and succinct way of determining where the atoms are in highly correlated states as fragmentation occurs, and are particularly helpful in understanding what is actually happening when energy levels with macroscopic occupancy cross as a function of breaking the symmetry between the trap wells. It is seen that only a few particles are actually active in the level crossing. Recent experiments in super-conductive Josephson loops showing tunneling of macroscopic quantum states are easily included in this picture.