Quantum Monte Carlo Methods In Condensed Matter Physics


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


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


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


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.







Lectures on the Physics of Strongly Correlated Systems XIV


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 III


Book Description

The contribution of computer simulation studies to our understanding of the prop erties of a wide range of condensed matter systems is now weIl established. The Center for Simulational Physics of the University of Georgia has been hosting a series of annual workshops with the intent of bringing together experienced prac titioners in the field, as weIl as relative newcomers, to provide a forum for the exchange of ideas and recent results. This year's workshop, the third in the series, was held February 12-16, 1990. These proceedings are arecord of the workshop and are published with the goal of timely dissemination of the papers to a wider audience. The proceedings are divided into four parts. The first contains invited pa pers dealing with simulational studies of classical systems and also includes an introduction to some new simulation techniques. Aseparate section is devoted to invited papers on quantum systems, including new results for strongly correlated electron and quantum spin models believed to be important for the description of high-Tc superconductors. The third part consists of a single invited paper, which presents a comprehensive treatment of issues associated with high perfor mance computing, including differences in architectures and a discussion of access strategies. The contributed papers constitute the final part.




Computer Simulation Studies in Condensed-Matter Physics IX


Book Description

Computer Simulation Studies in Condensed-Matter Physics IX covers recent developments in this field. This workshop was the ninth in this series and was held at the University of Georgia, March 4-9, 1996, and these proceedings form a record which is published with the goal of timely dissemination of the material to a wider audience. This volume is composed of three parts. The first section contains invited papers that deal with simulational studies of classical systems. The second section of the proceedings is devoted to invited papers on quantum systems, including new results for strongly correlated electron and quantum spin models. The final section comprises contributed presentations.