Spin liquids in quantum antiferromagnetic models on two dimensional frustrated lattices. - TEL - Thèses en ligne Accéder directement au contenu
Thèse Année : 2012

Spin liquids in quantum antiferromagnetic models on two dimensional frustrated lattices.

Liquides de spin dans les modèles antiferromagnétiques quantiques sur réseaux bi-dimensionnels frustrés

Résumé

For a long time the backbone of traditional condensed matter theory was comprised of two pieces. The first to be formulated was Landau's symmetry breaking theory, to be supplemented later by the theory of renormalization group and the second was Landau's Fermi liquid theory. For about half a century these two theories dominated condensed matter physics since people could not find a system that was not described by Landau's theories. The exceptional success of these theories lead to the belief that we understood in principle the structure and behavior of all forms of matter. The shock came in 1982 with the discovery of the fractional quantum Hall effect, wherein it was found that these fractional quantum Hall liquids exhibit non-Fermi liquid behavior. Furthermore, different fractional quantum Hall liquids have the same symmetries, and thus fall out of the realm of Landau's symmetry breaking theory. These discoveries marked a revolution in condensed matter theory and acted as a passage to a whole new world beyond Landau's theories. The frustrated low dimensional quantum spin systems provide a very promising playground to catch a glimpse of this new world of exotic non-Fermi liquid phases. These systems are examples of strongly correlated many body systems and have been argued to host states which lack long range order and do not spontaneously break any symmetries. These quantum spin liquid states contain completely new types of orders which are ''dynamic'' in origin, i.e. related to symmetries of complex ground state wave functions, as opposed to ''static'' positional crystalline orders which are related to symmetries of classical probability distribution functions of atoms, thus these novel orders are called ''quantum orders'' . In some cases quantum spin liquids also feature topological orders. One can alternatively view quantum orders as describing the pattern of quantum entanglement in the many-body ground state, in this picture the conventional crystalline phase lacks any non-trivial entanglement pattern. To this effect, the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice has been shown to host such an exotic quantum paramagnetic state. This is made possible through the combination of low spin, low dimensionality, low coordination number and frustrating antiferromagnetic interactions of the Heisenberg type, all of which combine to amplify quantum fluctuations to an extent needed to stabilize a quantum paramagnet, even at T=0. The near perfect realization of this model Hamiltonian is found in Herbertsmithite (${\rm Zn}{\rm Cu}_{3}{\rm (OH)}_{6}{\rm Cl}_{2}$) on which various probes have established a quantum spin liquid behavior down to temperatures of 20 mK ($\sim J/10^{4}$). However, the precise identification of this quantum paramagnetic phase is still an open problem experimentally and even more so theoretically where this question has and is being vigorously debated without any definitive conclusions, till date. Different approximate theoretical approaches have yielded myriad of different possible ground states, which have been found to be competing within a very narrow spectrum of energy, and are extremely sensitive to small perturbations. This extensive quasi-degeneracy of the ground state manifold is what makes the problem of the ground state of the kagome antiferromagnet an extremely challenging puzzle. In my thesis, I will revisit this problem within the realm of slave-particle approaches, which form the traditional line of attack for studying spin systems featuring a magnetically disordered ground state. In particular, I shall work within the SU(2) slave boson (Schwinger fermion) approach. Within this formalism, it was argued in that a particular algebraic spin liquid with a U(1) low energy gauge structure (so called U(1) Dirac spin liquid) possesses the lowest energy and should occur as the ground state. In fact, all experimental studies till date back up such a claim for a long range resonating valence bond state to be stabilized. However, such algebraic spin liquids are marginally stable and hence ''critical'', thus lending support to the thought that at least for spin-1/2 models such spin liquids should destabilize into either the class of stable Z2 spin liquids or into valence-bond crystals, and it has not been appreciated that such delicate phases can in fact be robust, and exist as real physical spin liquids. The existence of algebraic spin liquids is quite a remarkable and revolutionary phenomenon as it disproves conventional wisdom, and indirectly proves the existence of quantum orders which are in fact responsible for protecting the gapless nature of the spin liquid excitations. This is another reason which makes the kagome Heisenberg model not only challenging but also exciting, since it involves a frontier issue. The broad aim and conclusion of the work contained in the thesis is to study and demonstrate the remarkable stability of the U(1) Dirac spin liquid with respect to a very large class of perturbations, including Z2 spin liquids, valence bonds crystals and chiral spin liquids, and thus to vouch for it as the ground state of the spin-1/2 quantum Heisenberg model on the kagome lattice. The relevant numerical framework for tackling the above mentioned problems and issues is provided by the fermionic variational quantum Monte Carlo methods. In practice, we compute the energy of optimized variational wave functions that are constructed by applying the Gutzwiller projector to different states obtained from mean-field Hamiltonians of Schwinger fermions. In this respect, by an exact treatment of the full projector that ensures the one fermion per site constraint, we go much beyond the simple mean-field approach. To carry out the optimization of wave functions representing these competing phases I have used a state-of-the-art implementation of the stochastic reconfiguration optimization algorithm. This method enables one to obtain an extremely accurate determination of variational parameters, since small energy differences are effectively computed by using a correlated sampling, which makes it possible to strongly reduce statistical fluctuations. This feature is indispensable when one wants to literally ''hair split'' phases which are clustered together in a narrow energy width, as is the case with the kagome spin-1/2 Heisenberg antiferromagnet problem. We also did an extension of the above scheme, by implementing the Lanczos algorithm within a variational Monte Carlo framework, since, this is necessary to improve the variational wave functions and also to extract the true ground state properties.
La recherche de phases magnétiques exotiques de la matière qui fondent même à T = 0 uniquement sous l’action des fluctuations quantiques a été long et ardu, à la fois théorique- ment et expérimentalement. La percée est venue récemment avec la découverte de l’Herbert- smithite, un composé formant un réseau kagome parfait avec des moments magnétiques de spin-1/2. Des expériences pionnières, mêlant des mesures de NMR, μSR et de diffu- sion de neutrons, ont montré une absence totale de gel ou d’ordre des moments magné- tiques de spin, fournissant ainsi une forte signature d’une phase paramagnétique quantique. Théoriquement, l’Herbertsmithite est extrêmement bien modélisé par le modèle de Heisen- berg quantique antiferromagnétique pour des spins-1/2 sur le réseau kagome, problème qui n’a pas été résolu jusqu’à présent. Plusieurs méthodes approximatives numériques et ana- lytiques ont donné différents états fondamentaux, allant des liquides de spins Z2 gappés et un liquide de spins exotique algébrique U(1) de Dirac aux liquides de spins chiraux et les cristaux à liaisons de valence. Dans cette thèse, le problème est traité dans le cadre d’une approche particule-esclave fermionique, à savoir le formalisme des fermions de Schwinger SU(2). Il est conclu qu’un liquide de spins sans gap algébrique de Dirac a l’énergie varia- tionnelle la plus basse et peut en fait constituer un vrai état fondamental physique de liquide de spins. Une implémentation sophistiquée de méthodes numériques de pointes comme le Monte-Carlo variationnel, le Monte-Carlo fonctions de Green et l’application de pas Lanczos dans un schéma variationnel ont été utilisés. Il est montré que contrairement à la croyance habituelle, le liquide de spins de Dirac U(1) projeté en “2 + 1” dimensions est remarquable- ment robuste par rapport à une large classe de perturbations, incluant les liquides de spins topologiques Z2 et les cristaux à liaisons de valence. De plus, l’application de deux pas Lanczos sur la fonction d’onde du liquide de spins de Dirac U(1) montre que son énergie est compétitive avec celles proposées pour les liquides de spins topologiques Z2. Ce résultat, combiné avec les indications expérimentales qui pointent vers un liquide de spins sans gap pour l’Herbertsmithite, appuie l’affirmation que le vrai état fondamental de ce modèle est en fait un liquide de spins algébrique de Dirac
Fichier principal
Vignette du fichier
PhD-thesis-Yasir.pdf (11.2 Mo) Télécharger le fichier
Pres-defense.pdf (11.36 Mo) Télécharger le fichier
Format : Autre

Dates et versions

tel-00752096 , version 1 (14-11-2012)
tel-00752096 , version 2 (19-11-2013)

Identifiants

  • HAL Id : tel-00752096 , version 1

Citer

Yasir Iqbal. Spin liquids in quantum antiferromagnetic models on two dimensional frustrated lattices.. Strongly Correlated Electrons [cond-mat.str-el]. Université Paul Sabatier - Toulouse III, 2012. English. ⟨NNT : ⟩. ⟨tel-00752096v1⟩

Collections

IRSAMC LPT_FFC
702 Consultations
1748 Téléchargements

Partager

Gmail Facebook X LinkedIn More