Browsing by Subject "spin chains"
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(2021)Matrix product states provide an efficient parametrisation of lowentanglement manybody quantum states. In this thesis, the underlying theory is developed from scratch, requiring only basic notions of quantum mechanics and quantum information theory. A full introduction to matrix product state algebra and matrix product operators is given, culminating in the derivation of the density matrix renormalisation group algorithm. The latter provides a simple variational scheme to determine the ground state of arbitrary onedimensional manybody quantum systems with supreme precision. As an application of matrixproduct state technology, the kernel polynomial method is introduced in detail as a stateofthe art numerical tool to find the spectral function or the dynamical correlator of a given quantum system. This in turn gives access to the elementary excitations of the system, such that the locations of the lowenergy eigenstates can be studied directly in real space. To illustrate those theoretical tools concretely, the ground state energy, the entanglement entropy and the elementary excitations of a simple interface model of a Heisenberg ferromagnet and a Heisenberg antiferromagnet are studied. By changing the location of the model in parameter space, the dependence of the abovementioned quantities on the transverse field and the coupling strength is investigated. Most notably, we find that the entanglement entropy characteristic to the antiferromagnetic ground state stretches across the interface into the ferromagnetic halfchain. The dependence of the physics on the value of the coupling strength is, overall, small, with exception of the appearance of a boundary mode whose eigenenergy grows with the coupling. A comparison with a localised edge field shows however that the boundary mode is a true interaction effect of the two halfchains. Various algorithmic and physics extensions of the present project are discussed, such that the code written as part of this thesis could be turned into a stateoftheart MPS library with managable effort. In particular, an application of the kernel polynomial method to calculate finitetemperature correlators is derived in detail.
Now showing items 11 of 1