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6816 results in Condensed Matter Physics, Nanoscience and Mesoscopic Physics

Page 7 of 341

Theory of Liquids
  • From Excitations to Thermodynamics
  • Kostya Trachenko
  • Published online:
    01 September 2023
    Print publication:
    17 August 2023
  • Of the three basic states of matter, liquid is perhaps the most complex. While its flow properties are described by fluid mechanics, its thermodynamic properties are often neglected, and for many years it was widely believed that a general theory of liquid thermodynamics was unattainable. In recent decades that view has been challenged, as new advances have finally enabled us to understand and describe the thermodynamic properties of liquids. This book explains the recent developments in theory, experiment and modelling that have enabled us to understand the behaviour of excitations in liquids and the impact of this behaviour on heat capacity and other basic properties. Presented in plain language with a focus on real liquids and their experimental properties, this book is a useful reference text for researchers and graduate students in condensed matter physics and chemistry as well as for advanced courses covering the theory of liquids.

  • 9 - DMRG with Nonlocal Basis States

  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book:
    Density Matrix and Tensor Network Renormalization
    Published online:
    18 January 2024
    Print publication:
    31 August 2023, pp 137-153

  • Summary

    This chapter extends DMRG from real space to an arbitrary basis space in which each basis state, such as a momentum eigenstate or a molecular orbital, serves as an effective lattice site. Unlike in real space, the interaction potentials become nonlocal and off-diagonal in an arbitrary basis representation. To solve this nonlocal problem, one should optimize the order of basis states and introduce the so-called complementary operators to minimize the number of operators whose matrix elements must be computed and stored. We illustrate the momentum-space DMRG using the Hubbard model and discuss its application in other interacting fermion models. Finally, we introduce a DMRG scheme for optimizing the single-particle basis states and their order simultaneously in a more general basis space without momentum conservation.

Page 7 of 341