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Title:  Correlations in interacting and in open quantum systems
Author:  Tianqi Chen
As Contributor:   Tianqi Chen
Type: Ph.D.
Field: Physics
  • Quantum Physics
Approaches: Theoretical, Computational
Degree granting institution:  Singapore University of Technology and Design
Supervisor(s): Dario Poletti
Defense date:  2021-11-03


Correlations emerging in condensed matter systems can lead to intriguing physical phenomena such as exotic phases of matter, electron transport in metals and energy transfer in nanoscale devices. In this thesis, we strive to explore two distinct means of investigating correlations in quantum many-body systems: through interactions within the system, and external sources. Firstly, in a closed system, the effect of nonuniform Dzyaloshinskii-Moriya (DM) interactions on correlations in a quasi-2D Shastry- Sutherland model is studied via matrix product state based ground state search algorithm. The non-number-conserving intradimer DM interactions make the shape of the magnetization curve smooth, while the number-conserving interdimer DM interactions induce different small plateaux, which are signatures of the finite size of the sys- tem. This is revealed through the investigation of dimer correlation functions. The in- terdimer DM interactions also induce chirality in the system where the chirality phase is identified. Then, in the presence of a quantum system connected to external environment, the transport properties of an anharmonic oscillator coupled to two different thermal baths is studied using the numerically exact approaches such as thermofield based chain-mapping matrix product states (TCMPS). The effect of bath temperature bias, system-bath coupling strength, as well as on-site interactions on the steady-state transport properties is shown, as well as evidence of non-Markovian dynamics probed by the nonmonotonicity of the time evolution of the trace distance between two different initial states. Finally, moving towards a time-dependent system, a harmonic oscillator under periodic driving and coupled to two heat baths at different temperatures is studied. Using the same thermofield transformation with chain mapping approach for this setup, the emergence of periodic steady state is shown. The system can be tuned from an engine to an accelerator or even to a heater by changing the system and the bath parameters. The steady-state correlations that emerge between the system and the baths, as well as those that grow between the baths are also presented.

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