Werner Heisenberg | EPFL Graph Search

Werner Heisenberg, né le à Wurtzbourg (Empire allemand) et mort le à Munich (Allemagne de l'Ouest), est un physicien allemand qui est l'un des fondateurs de la mécanique quantique, notamment en mettant en évidence le principe d'incertitude et en développant la formulation probabiliste de la fonction d'onde. Pendant la Seconde Guerre mondiale, il participe aux recherches atomiques sous le Troisième Reich et fait de la propagande en faveur de l'Allemagne nazie. Capturé après la guerre, il est relâché après plusieurs mois de captivité et retourne en Allemagne, où il poursuit une carrière académique. Il est lauréat du prix Nobel de physique de 1932 . Selon des scientifiques et des historiens, Heisenberg n'avait aucun scrupule à développer une bombe atomique pour le compte du régime nazi, mais ce jugement n'est pas largement partagé parmi les spécialistes. Biographie Enfance Werner Karl Heisenberg naît le 5 décembre 1901 à Würtzburg dans une famille d'enseignants

Emergent multipolar spin correlations in a fluctuating spiral: The frustrated ferromagnetic spin-1/2 Heisenberg chain in a magnetic field

We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J(1)-J(2) chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states toward spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional S=1/2 quantum magnets in a magnetic field.

2009

Exact diagonalization of SU( N ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( N ) symmetry

Frédéric Mila, Pierre Marcel Nataf, Kianna Wan

We present a method for the exact diagonalization of the SU(N) Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global SU(N) group. This generalized scheme is applicable to chains consisting of several particles per site, with any SU(N) symmetry at each site. Extending some of the key results of substitutional analysis, we demonstrate how basis states can be efficiently constructed for the relevant SU(N) subsector, which, especially with increasing values of N or numbers of sites, has a much smaller dimension than the full Hilbert space. This allows us to analyze systems of larger sizes than can be handled by existing techniques. We apply this method to investigate the presence of edge states in SU(N) Heisenberg and Affleck-Kennedy-Lieb-Tasaki Hamiltonians.

2017

Uncovering the Physics of Frustrated Quantum Magnets using the Correlation Density Matrix Approach

This work is devoted to the study, the development, and the application of a new systematic method yielding the dominant correlations that govern a quantum many-body state in an unbiased way. The dominant correlations between any two disjoint blocks of a system are extracted by performing a singular value decomposition of the correlation density matrix (CDM) between those blocks. We determine several mathematical properties and features of this method, in particular the consequences of the lattice symmetries or the symmetries intrinsic to the studied state on the singular values spectrum. We investigate the relation between the norm of the CDM – providing a natural measure of the total correlation between the two blocks – and the so-called mutual information, a quantity originally introduced in quantum information theory. This novel tool is utilized for sheding new light on the zero temperature physics of the spin-1/2 frustrated ferromagnetic J1–J2 Heisenberg chain in a magnetic field as well as on the low-energy physics of the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional kagomé lattice. The states are computed using exact diagonalization and the density matrix renormalization group procedure in the first case, and exact diagonalization only in the second case. This work is introduced in Chapter 1. The first model is then presented in Chapter 2. Chapter 3 introduces the CDM method, and Chapter 4 is devoted to the study of the kagomé antiferromagnet. In the J1–J2 chain, we reveal a vector chiral phase at low magnetic field and a sequence of multipolar Luttinger liquid phases at high field. We explicitly show that these multipolar phases result from the destabilization – driven by a locking mechanism – of the classical spiral ground state in the absence of magnetic field. This point of view is completely new: multipolar phases were known to be a possible destabilization of ferromagnetic phases, but they have never been reported as a destabilization of spiral states yet. Regarding the kagomé antiferromagnet, we address for the first time the question of the nature of the singlet states forming its quite dense singlet spectrum above the ground state. We show that some of these low-lying singlet states have large dimer correlations which do not seem to significantly decrease with the distance, moreover our CDM studies confirm that the dominant correlations in those singlet states are of the dimer-dimer type. Studies of Von Neumann block entropies reveal a very short correlation length on the one hand, and entropies that are roughly independent on the energy of the state under consideration on the other hand. The scenario of a valence bond crystal phase is investigated and the relevance of different kinds of crystals (from the literature or ad hoc) for reproducing the dimer correlations in the 36-site sample is probed.

EPFL2010

Uncovering the Physics of Frustrated Quantum Magnets using the Correlation Density Matrix Approach

EPFL2010