The Flow Equation Approach To Many Particle Systems
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The Flow Equation Approach to Many-Particle Systems
Overthepastdecade,the?owequationmethodhasdevelopedintoanewv- satile theoretical approach to quantum many-body physics. Its basic concept was conceived independently by Wegner [1] and by G lazek and Wilson [2, 3]: the derivation of a unitary ?ow that makes a many-particle Hamiltonian - creasingly energy-diagonal. This concept can be seen as a generalization of theconventionalscalingapproachesinmany-bodyphysics,wheresomeult- violet energy scale is lowered down to the experimentally relevant low-energy scale [4]. The main di?erence between the conventional scaling approach and the ?ow equation approach can then be traced back to the fact that the ?ow equation approach retains all degrees of freedom, i. e. the full Hilbert space, while the conventional scaling approach focusses on some low-energy subspace. One useful feature of the ?ow equation approach is therefore that it allows the calculation of dynamical quantities on all energy scales in one uni?ed framework. Since its introduction, a substantial body of work using the ?ow eq- tion approach has accumulated. It was used to study a number of very d- ferent quantum many-body problems from dissipative quantum systems to correlated electron physics. Recently, it also became apparent that the ?ow equation approach is very suitable for studying quantum many-body n- equilibrium problems, which form one of the current frontiers of modern theoretical physics. Therefore the time seems ready to compile the research literature on ?ow equations in a consistent and accessible way, which was my goal in writing this book.
The Flow Equation Approach to Many-Particle Systems
Author: Stefan Kehrein
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-07-07
This self-contained introduction addresses the novel flow equation approach for many particle systems and provides an up-to-date review of the subject. The text first discusses the general ideas and concepts of the flow equation method, and then in a second part illustrates them with various applications in condensed matter theory. The third and last part of the book contains an outlook with current perspectives for future research.
Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems
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.