Author: Stefanie CzischekPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Simulating Strongly Interacting Quantum Spin Systems
Author: Stefanie CzischekSimulating Strongly Interacting Quantum Spin Systems
Author: Stefanie CzischekQuantum Monte Carlo Methods In Condensed Matter Physics
Author: Masuo SuzukiPublisher: World Scientific
ISBN: 9814602337
Category : Science
Languages : en
Pages : 378
Book Description
This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-Tc superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.
Neural-Network Simulation of Strongly Correlated Quantum Systems
Author: Stefanie CzischekPublisher: Springer Nature
ISBN: 3030527158
Category : Science
Languages : en
Pages : 205
Book Description
Quantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.
Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems
Author: Laurens VanderstraetenPublisher: Springer
ISBN: 3319641913
Category : Science
Languages : en
Pages : 229
Book Description
This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.
Computer Simulation Studies in Condensed-Matter Physics VIII
Author: David P. LandauPublisher: Springer Science & Business Media
ISBN: 3642799914
Category : Science
Languages : en
Pages : 185
Book Description
Computer Simulation Studies in Condensed-Matter Physics VIII covers recent developments in this field presented at the 1995 workshop, such as new algorithms, methods of analysis, and conceptual developments. This volume is composed of three parts. The first part contains invited papers that deal with simulational studies of classical systems. The second part is devoted to invited papers on quantum systems, including new results for strongly correlated electron and quantum spin models. The final part comprises contributed presentations.
Shaping the Hamiltonian of Many-body Spin Systems on a Rydberg-atom Quantum Simulator
Author: Sebastian GeierLectures on the Physics of Strongly Correlated Systems XIV
Author: Adolfo AvellaPublisher: American Institute of Physics
ISBN: 9780735408517
Category : Technology & Engineering
Languages : en
Pages : 0
Book Description
The volume contains the lectures delivered at the XIV Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2009. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographs of relevant subjects in the field of Condensed Matter Physics. Contributions include: Electronic Structure of Strongly Correlated Materials (Electronic structure calculations in one-electron approximation; Hubbard model in Dynamical Mean-Field Theory (DMFT); Electronic structure calculations for real materials by LDA+DMFT method); Computational Studies of Quantum Spin Systems (Quantum spin models, their ground states and quantum phase transitions; Classical phase transitions, Monte Carlo simulations, and finite-size scaling; Exact diagonalization methods; Quantum Monte Carlo simulations and the Stochastic Series Expansion method; Survey of related computational methods); Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials (Mean-field theories for many-body systems; Lattice fermions in the limit of high dimensions; Dynamical mean-field theory for correlated lattice fermions; The Mott-Hubbard Metal-Insulator Transition; Electronic correlations and disorder; Theory of electronic correlations in materials; Kinks in the dispersion of strongly correlated electron systems).
Computer Simulation Studies in Condensed-Matter Physics X
Author: David P. LandauPublisher: Springer Science & Business Media
ISBN: 3642468519
Category : Science
Languages : en
Pages : 274
Book Description
Computer Simulation Studies in Condensed-Matter Physics X is devoted to Prof. Masuo Suzuki's ideas, which have made novel, new simulations possible. These proceedings, of the 1997 workshop, comprise three parts that deal with new algorithms, methods of analysis, and conceptual developments. The first part contains invited papers that deal with simulational studies of classical systems. The second of the proceedings is devoted to invited papers on quantum systems, including new results for strongly correlated electron and quantum spin models. The final part contains a large number of contributed presentations.
Strongly Interacting Quantum Systems out of Equilibrium
Author: Thierry GiamarchiPublisher: Oxford University Press
ISBN: 0191080535
Category : Science
Languages : en
Pages : 607
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.