Strongly-correlated lattice systems on a finite cylinder
<p>In this thesis, I present my research on the numerical simulation of finite-size strongly-correlated lattice systems using the density matrix renormalisation group (DMRG). Ultracold gases in optical lattices have become the experimental setup of choice to simulate models from condensed-matt...
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| Formato: | Thesis |
| Idioma: | English |
| Publicado: |
2019
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| Summary: | <p>In this thesis, I present my research on the numerical simulation of finite-size
strongly-correlated lattice systems using the density matrix renormalisation group
(DMRG). Ultracold gases in optical lattices have become the experimental setup of
choice to simulate models from condensed-matter physics, because of their high degree
of tunability and control. Their inherently finite size and alternative implementation
call for a more in-detail study of how to define and characterise the phases of the
models that they simulate.<p>
<p>I use DMRG to implement lattice Hamiltonians of highly-correlated systems with
long-range interactions and identify their ground states on a finite system geometry.
I describe in detail the process of constructing long-range Hamiltonians for their use
in DMRG. I then apply these numerical methods to two fundamental models. I study
the ground state of a fractional quantum Hall system and identify it as the well-known
Laughlin state in a still unexplored parameter regime, by calculating its topological
entanglement entropy and by using a set of physical observables that are available in a
finite cylindrical geometry. I then study a dipolar Bose-Hubbard model and perform
a systematic study of the order parameters that can best be used to characterise its
phases in an ultracold gas setting by comparing how different types of observables
are sensitive to finite-size and boundary effects.
My results are meant to provide guidance for future experimental realisations of
bosonic lattice models of small sizes.<p> |
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