Subsequent projects | Special projects

Start of funding 01.01.2017

Emergent phenomena in correlated quantum matter

Prof. Dr. Fakher Assaad
University of Würzburg
Fakultät für Physik und Astronomie

Prof. Dr. Tarun Grover
University of California, San Diego
Department of Physics


A rich variety of phases beyond solid, liquid, and gas are found in nature, and these phases originate from simple rules that encode interactions among elementary constituents. Quantum mechanics provides a window to new phases in which constituents can be in several different patterns all at once, much like Schrödinger’s cat can be dead and alive simultaneously. These simple rules define multi-scale problems where new emergent phases occur at low energies. Emergent phases are interesting since collective excitations have no relation to the elementary constituents we started of with. In this project we will consider a set of models (i.e. simple rules) that can be solved in polynomial time using state-of-the-art Quantum Monte Carlo simulations. We expect these models to have complicated phase diagrams harboring many emergent states of matter. Our aim is to compute the phase diagrams and ultimately to understand the nature of quantum phase transitions.

Final report:
The goal of our project was to build on advances in quantum Monte Carlo methods to investigate a class of phenomena where electronic correlations play a decisive role. We set off to formulate models amenable to negative sign free Monte Carlo simulations that violate fundamental theorems in the solid state. To achieve this, we first had to develop tools that enabled us to consider very general systems of electrons Kondo coupled to spin 1/2 degrees of freedom [2]. This describes, for example, magnetic adatoms on metallic surfaces. With these developments we could consider frustrated spin models that are described by an emergent Z2 lattice gauge theory in its deconfined phase [1]. The Kondo coupling between these spins and a sea of conduction electrons lead to the so-called FL* phase, realized in Ref. [3], and that violates the Luttinger sum rule. This exotic phase of matter is one of the candidate states of matter to describe the Kondo breakdown in heavy fermion materials. On the whole this project was very successful. It led to a number of publications in high level peer reviewed journals and contributed to the education of Postdoctoral fellows and PhD students.

[1] F. F. Assaad and Tarun Grover, Simple Fermionic Model of Deconfined Phases and Phase Transitions, Phys. Rev. X 6 (2016), 041049.
[2] Toshihiro Sato, Fakher F. Assaad, and Tarun Grover, Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models, Phys. Rev. Lett. 120 (2018), 107201.
[3] Johannes S. Hofmann, Fakher F. Assaad, and Tarun Grover, Fractionalized Fermi Liquid in a Frustrated Kondo Lattice Model, Phys. Rev. B 100 (2019), 035118.