{"product_id":"density-matrix-and-tensor-network-renormalization-hardback-9781009398701","title":"Density Matrix and Tensor Network Renormalization (Hardback) 9781009398701","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eDensity Matrix and Tensor Network Renormalization\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAn introduction to tensor network renormalization, a powerful tool for the study of quantum many-body problems and complex systems.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eTao Xiang (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009398701, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 31 July 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e470 pages\u003cbr\u003e28 x 19 x 2.9 cm, 0.883 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eRenormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Abbreviations\u003cbr\u003e Unit used\u003cbr\u003e Notations and graphical representations\u003cbr\u003e 1. Introduction\u003cbr\u003e 2. Basic algebra of tensors\u003cbr\u003e 3. Tensor network representation of classical statistical methods\u003cbr\u003e 4. Tensor-network ansatz of wave functions\u003cbr\u003e 5. Criterion of truncation: symmetric systems\u003cbr\u003e 6. Real-space DMRG\u003cbr\u003e 7. Implementation of symmetries\u003cbr\u003e 8. DMRG with non-local basis states\u003cbr\u003e 9. Matrix Product States\u003cbr\u003e 10. Infinite Matrix Product States\u003cbr\u003e 11. Determination of MPS\u003cbr\u003e 12. Continuous Matrix Product States\u003cbr\u003e 13. Classical Transfer Matrix Renormalization\u003cbr\u003e 14. Criterion of truncation: non-symmetric systems\u003cbr\u003e 15. Renormalization of quantum transfer matrices\u003cbr\u003e 16. MPS solution of QTMRG\u003cbr\u003e 17. Dynamical Correlation Functions\u003cbr\u003e 18. Time-dependent methods\u003cbr\u003e 19. Tangent-space operations\u003cbr\u003e 20. Tangent-space approaches\u003cbr\u003e 21. Tree Tensor Network States\u003cbr\u003e 22. Two-dimensional tensor network states\u003cbr\u003e 23. Coarse graining tensor renormalization\u003cbr\u003e Appendix A\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Condensed matter physics [\u003ca title=\"See our other books on Condensed matter physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Condensed%20matter%20physics%20%5Bliquid%20state%20\u0026amp;%20solid%20state%20physics%5D%20%5BPHFC%5D%22\"\u003eliquid state \u0026amp; solid state physics PHFC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46334655004952,"sku":"9781009398701","price":51.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781009398701i.jpg?v=1692411874","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/density-matrix-and-tensor-network-renormalization-hardback-9781009398701","provider":"Freshly Printed Books","version":"1.0","type":"link"}