A defining feature of quantum many-body systems is the presence of entanglement among their constituents. Besides providing valuable insights on several physical properties, entanglement is also responsible for the computational complexity of simulating quantum systems with variational methods. This thesis explores several aspects of entanglement in many-body systems, with the primary goal of devising efficient approaches for the study of topological properties and quantum dynamics of lattice models.
The first focus of this work is the development of variational wavefunctions inspired by artificial neural networks. These can efficiently encode long-range and extensive entanglement in their structure, as opposed to the case of tensor network states. This feature makes them promising tools for the study of topologically ordered phases, quantum critical states as well as dynamical properties of quantum systems. In this thesis, we characterize the representational power of a specific class of artificial neural network states, constructed from Boltzmann machines. First, we show that wavefunctions obtained from restricted Boltzmann machines can efficiently parametrize chiral topological phases, such as fractional quantum Hall states. We then turn our attention to deep Boltzmann machines. In this framework, we propose a new class of variational wavefunctions, coined generalized transfer matrix states, which encompass restricted Boltzmann machine and tensor network states. We investigate the entanglement properties of this ansatz, as well as its capability of representing physical states.
Understanding how the entanglement properties of a system evolve in time is the second focus of this thesis. In this context, we first investigate the manifestation of topological properties in the unitary dynamics of systems after a quench, using the degeneracy of the entanglement spectrum as a possible signature. We then analyze the phenomenon of entanglement growth, which limits to short timescales the applicability of tensor network methods in out-of-equilibrium problems. We investigate whether these limitations can be overcome by exploiting the dependence of entanglement entropies on the chosen computational basis. Specifically, we study how the spreading of quantum correlations can be contained by means of time-dependent basis rotations of the state, using exact diagonalization to simulate its dynamics after a quench. Going beyond the case of sudden quenches, we then show how, in certain weakly interacting problems, the asymptotic value of the entanglement entropy can be tuned by modifying the velocity at which the parameters in the Hamiltonian are changed. This enables the simulation of longer timescales using tensor network approaches. We present preliminary results obtained with matrix product states methods, with the goal of studying how equilibration affects the transport properties of interacting systems at long times.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:76132 |
| Date | 01 October 2021 |
| Creators | Pastori, Lorenzo |
| Contributors | Budich, Jan Carl, Bardarson, Jens, TU Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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