The Effects of Disorder in Strongly Interacting Quantum Systems PDF Download
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Author: Steven J. Thomson
Publisher:
ISBN:
Category : Condensed matter
Languages : en
Pages : 173
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Book Description
Author: Steven J. Thomson
Publisher:
ISBN:
Category : Condensed matter
Languages : en
Pages : 173
Get Book Here
Book Description
Author: Steven J. Thomson
Publisher:
ISBN:
Category : Condensed matter
Languages : en
Pages : 0
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Book Description
Author:
Publisher:
ISBN:
Category : Family & Relationships
Languages : en
Pages : 0
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Book Description
This Book contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.
Author: Thierry Giamarchi
Publisher: Oxford University Press
ISBN: 0198768168
Category : Science
Languages : en
Pages : 607
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Book Description
This book presents new experimental tools and theoretical concepts of collective nonequilibrium behavior of quantum systems. The book is based on the Les Houches Summer School of August 2012, "Strongly interacting quantum systems out of equilibrium".
Author: Thierry Giamarchi
Publisher: Oxford University Press
ISBN: 0191080543
Category : Science
Languages : en
Pages : 464
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Book Description
Over the last decade new experimental tools and theoretical concepts are providing new insights into collective nonequilibrium behavior of quantum systems. The exquisite control provided by laser trapping and cooling techniques allows us to observe the behavior of condensed bose and degenerate Fermi gases under nonequilibrium drive or after `quenches' in which a Hamiltonian parameter is suddenly or slowly changed. On the solid state front, high intensity short-time pulses and fast (femtosecond) probes allow solids to be put into highly excited states and probed before relaxation and dissipation occur. Experimental developments are matched by progress in theoretical techniques ranging from exact solutions of strongly interacting nonequilibrium models to new approaches to nonequilibrium numerics. The summer school `Strongly interacting quantum systems out of equilibrium' held at the Les Houches School of Physics as its XCIX session was designed to summarize this progress, lay out the open questions and define directions for future work. This books collects the lecture notes of the main courses given in this summer school.
Author: Assa Auerbach
Publisher: Springer Science & Business Media
ISBN: 1461208696
Category : Science
Languages : en
Pages : 249
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Book Description
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.
Author: Chao Wang (Researcher of quantum many-body physics)
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Strongly correlated electron systems are one of the central topics of condensed matter physics. The myriad of combinations of diverse Fermiologies, phonon spectra and electron-electron, electron-phonon interactions, together with spin-orbit couplings, Kondo couplings, and effects of disorder and external magnetic fields, leads to a truly dazzling range of quantum many-body phenomena. Superconductivity (conventional and unconventional) and magnetism are among the most prominent examples of quantum phases of matter that occur in such systems. We know that powerful emergent principles such as symmetry and topology are required to explain these emergent phenomena. However, due to the inherent difficulty of studying systems with macroscopically large number of strongly interacting particles, there remains the challenge of connecting these somewhat abstract mathematical principles with the underlying microscopic interactions. In this thesis, we illustrate, through two examples of systems with electron-electron and electron-phonon interactions, how one can simplify intractable quantum chemistry problems by reducing them to effective model Hamiltonians that capture the essence of microscopic interactions important to low-energy excitations, which we can then study using a variety of tools, such as determinantal quantum Monte Carlo (DQMC), exact diagonalization, weak and strong coupling considerations and mean-field theory. In the first example we encounter a novel deconfined quantum critical point (DQCP) with emergent O(4) symmetry. In the second example we offer a phenomenological explanation of superconducting and insulating phases of twisted bilayer graphene. Lastly, we also visit the more field-theoretic problem of boson-fermion duality in two spatial dimensions, for which we provide an exact lattice construction. This duality is closely related to the half-filled Landau level problem in quantum Hall physics.
Author: Manuel Valiente
Publisher:
ISBN: 9780750330923
Category : Science
Languages : en
Pages : 0
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Book Description
Author: Bo Xiao
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Electron-electron and electron-phonon interactions play fundamental roles in condensed matter physics. Strong correlations among electrons and between electrons and phonons lead to beautiful emergent phenomena both in materials and in the models used to describe them. Unfortunately, the complexity induced from the combination of interactions and large numbers of degrees of freedom makes analytically solving these models very difficult, even when greatly simplified. As a consequence, many important questions in many-body physics remain open. For example, the discoveries of charge density wave (CDW) in the pseudogap phase of the unconventional high-temperature cuprate superconductors motivate on-going research on electron-phonon interactions and its effects on the off-diagonal long-range order (ODLRO). In conventional superconductors, the attractive interaction between electrons which is mediated by the electron-phonon interaction is essential for the formation of Cooper pairs. However, if the electron-phonon interaction is sufficiently strong, charge order emerges near commensurate filling to compete with superconductivity. In this thesis, we use a combination of numerical and analytical methods to understand this sort of interplay between different types of order in the microscopic and macroscopic behavior of many-body systems. In Chapter 1, we introduce the Hubbard and Holstein Hamiltonians and the some of the exotic phases and phase transitions which they describe. We also build up some of the connections between numerical solutions of these models and experimental results for superconducting, charge, and spin order. In Chapter 2 and 3, we set up the frameworks of quantum Monte Carlo (QMC) algorithms and machine learning (ML) methods. We show how to translate a quantum-mechanical problem into an algorithm with analytical analysis encoded in it, which can be widely applied to various models and physics. In Chapter 4 and 5, we quantitatively determine the phase diagrams of one dimensional electron-phonon models where electrons have a long-range coupling to phonons as well as repulsive electron-electron interactions. We analyze the resulting metallic, Mott insulator, Peierls insulator phases, as well as the phase separation which we show often arises from momentum-dependent electron-phonon coupling. Although much work has been done on the extended Hubbard model, our research on including electron-phonon interactions pushes the field in a new direction. In Chapter 6, we describe the first study of the interplay between electron-phonon interaction and the effects of randomness. Our central result is a somewhat unexpected one: the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. In Chapter 7, we use QMC and cutting-edge ML methods to identify phase transitions involving 'off-diagonal' order parameters using 'diagonal' order parameter descriptors. Our study has implications for the exploration of strong correlations using quantum gas microscopy (QGM). Chapter 8 summarizes some of the key results of this thesis, and points areas of investigation which would be important to pursue further. The material presented in Chapters 3, 4 and 5 of this dissertation is based on two published articles in Physical Review B, references [1, 2], and one manuscript which has been submitted and is under review at Physical Review Letters, reference [3]. Chapter 7 is based on reference [4], which is in preparation.
Author: Igor V. Lerner
Publisher: Springer Science & Business Media
ISBN: 9401005303
Category : Science
Languages : en
Pages : 405
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Book Description
The physics of strongly correlated fermions and bosons in a disordered envi ronment and confined geometries is at the focus of intense experimental and theoretical research efforts. Advances in material technology and in low temper ature techniques during the last few years led to the discoveries of new physical of atomic gases and a possible metal phenomena including Bose condensation insulator transition in two-dimensional high mobility electron structures. Situ ations were the electronic system is so dominated by interactions that the old concepts of a Fermi liquid do not necessarily make a good starting point are now routinely achieved. This is particularly true in the theory of low dimensional systems such as carbon nanotubes, or in two dimensional electron gases in high mobility devices where the electrons can form a variety of new structures. In many of these sys tems disorder is an unavoidable complication and lead to a host of rich physical phenomena. This has pushed the forefront of fundamental research in condensed matter towards the edge where the interplay between many-body correlations and quantum interference enhanced by disorder has become the key to the understand ing of novel phenomena.
