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

Thèse EPFL

Résumé

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.

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Phase diagram of the two-dimensional antiferromagnet Ni-5(TeO3)(4)Br-2 with triangular arrangement of Ni2+ (S=1) magnetic moments within the [Ni5O17Br2] subunits has been investigated by temperature and magnetic field dependent heat-capacity, magnetization, and magnetic-torque measurements down to 1.5 K and up to 23 T. A nonzero magnetic contribution to the heat capacity observed up to 2.3T(N) is consistent with short-range magnetic ordering and the two-dimensional nature of the system. Below the Neel temperature T-N=29 K several antiferromagnetic phases were identified. The zero-field phase is characterized by a planar antiferromagnetic arrangement of the two in-layer neighboring [Ni5O17Br2] magnetic clusters within the magnetic unit cell. When the magnetic field is applied along the a(*) crystal axis, a spin-flop-like transition to a phase with a complex out-of-plane arrangement of Ni2+ (S=1) magnetic moments occurs at similar to 10 T. Using a molecular-field approach we predict that this transition will shift to higher fields with increasing temperature and that a magnetic phase with ferromagnetic ordering of [Ni5O17Br2] magnetic clusters will occur above 24 T. We ascribe the richness of the magnetic phases to strongly exchange-coupled clusters, being the basic building blocks of the investigated layered system.

2009Francesco Cerutti, Nikolaos Charitonidis, André Donadon Servelle, Philippe Jean Schoofs

FLUKA is a general purpose Monte Carlo code able to describe the transport and interaction of any particle and nucleus type in complex geometries over an energy range extending from thermal neutrons to ultrarelativistic hadron collisions. It has many different applications in accelerator design, detector studies, dosimetry, radiation protection, medical physics, and space research. In 2019, CERN and INFN, as FLUKA copyright holders, together decided to end their formal collaboration framework, allowing them henceforth to pursue different pathways aimed at meeting the evolving requirements of the FLUKA user community, and at ensuring the long term sustainability of the code. To this end, CERN set up the FLUKA.CERN Collaboration (1) . This paper illustrates the physics processes that have been newly released or are currently implemented in the code distributed by the FLUKA.CERN Collaboration (2) under new licensing conditions that are meant to further facilitate access to the code, as well as intercomparisons. The description of coherent effects experienced by high energy hadron beams in crystal devices, relevant to promising beam manipulation techniques, and the charged particle tracking in vacuum regions subject to an electric field, overcoming a former lack, have already been made available to the users. Other features, namely the different kinds of low energy deuteron interactions as well as the synchrotron radiation emission in the course of charged particle transport in vacuum regions subject to magnetic fields, are currently undergoing systematic testing and benchmarking prior to release. FLUKA is widely used to evaluate radiobiological effects, with the powerful support of the Flair graphical interface, whose new generation (Available at http://flair.cem) offers now additional capabilities, e.g., advanced 3D visualization with photorealistic rendering and support for industry-standard volume visualization of medical phantoms. FLUKA has also been playing an extensive role in the characterization of radiation environments in which electronics operate. In parallel, it has been used to evaluate the response of electronics to a variety of conditions not included in radiation testing guidelines and standards for space and accelerators, and not accessible through conventional ground level testing. Instructive results have been obtained from Single Event Effects (SEE) simulations and benchmarks, when possible, for various radiation types and energies. The code has reached a high level of maturity, from which the FLUKA.CERN Collaboration is planning a substantial evolution of its present architecture. Moving towards a modern programming language allows to overcome fundamental constraints that limited development options. Our long term goal, in addition to improving and extending its physics performances with even more rigorous scientific oversight, is to modernize its structure to integrate independent contributions more easily and to formalize quality assurance through state-of-the-art software deployment techniques. This includes a continuous integration pipeline to automatically validate the codebase as well as automatic processing and analysis of a tailored physics-case test suite. With regard to the aforementioned objectives, several paths are currently envisaged, like finding synergies with Geant4, both at the core structure and interface level, this way offering the user the possibility to run with the same input different Monte Carlo codes and crosscheck the results.

In spin systems, geometrical frustration describes the impossibility of minimizing simultaneously all the interactions in a Hamiltonian, often giving rise to macroscopic ground-state degeneracies and emergent low-temperature physics. In this thesis, combining tensor network (TN) methods to Monte Carlo (MC) methods and ground-state energy lower bound approaches, we study two-dimensional frustrated classical Ising models. In particular, we focus on the determination of the residual entropy in the presence of farther-neighbor interactions in kagome lattice Ising antiferromagnets (KIAFM).In general, using MC to determine the residual entropy is a significant challenge requiring ad-hoc updates, a precise evaluation of the energy at all temperatures to allow for thermodynamic integration, and a good control of the finite-size scaling behavior. As an alternative, we turn to TNs; however, we argue that, in the presence of frustration and macroscopic ground-state degeneracy, standard algorithms fail to converge at low temperatures on the usual TN formulation of partition functions. Inspired by methods for constructing ground-state energy lower bounds, we propose a systematic way to find the ground-state local rule using linear programming. Characterizing the rules as tiles that can be tessellated to form ground states of the model gives rise to a natural contractible TN formulation of the partition function. This method provides a direct access to the ground-state properties of frustrated models and, in particular, allows an extremely precise determination of their residual entropy.We then study two models inspired by artificial spin systems on the kagome lattice with out-of-plane (OOP) anisotropy. The first model is motivated by experiments on an array of chirally coupled nanomagnets. We argue that the farther-neighbor to nearest-neighbor couplings ratios in this system are much smaller than in the dipolar case, J2/J1 being of the order of 2%. A comparison of the experimental correlations with the results of extensive TN and MC simulations shows that (1) the experimental second- and third-neighbor correlations are inverted as compared to those of a pure nearest-neighbor model at equilibrium (even with a magnetic field), and (2) second-neighbor couplings as small as 1% of the nearest-neighbor couplings will affect the spin-spin correlations even at fairly high temperatures.Motivated by dipolar coupled artificial spin systems, we turn to the progressive lifting of the ground-state degeneracy of the KIAFM. We provide a detailed study of the ground-state phases of this model with up to third neighbor interactions, for arbitrary J2, J3 such that J1 >> J2, J3, obtaining exact results for the ground-state energies. When all couplings are antiferromagnetic, we exhibit three macroscopically degenerate ground-state phases and establish their residual entropy using our TN approach. Furthermore, in the phase corresponding to the dipolar KIAFM truncated to third neighbors, we use the ground-state tiles to establish the existence of a mapping to the ground-state manifold of the triangular Ising antiferromagnet.