Thesis
Dissipative and PT-symmetry breaking phase transitions in open spin systems
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2024
- Thesis identifier
- T17038
- Person Identifier (Local)
- 202057279
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- This thesis is concerned both with investigating the effects an environment has on quantum systems as well as with methods for the study of open quantum systems. In experiments and applications it is impossible to separate a quantum system from its environment. This often causes decoherence and loss of information, however, environments can also be used to drive systems into novel states which cannot otherwise be realized in Hamiltonian systems. In the first part of the thesis the effects of environments are studied by constructing a model which possess both an equilibrium-connected phase transition as well as a PT-symmetry breaking phase transition. The latter depends on the fine balance of gain and loss, and can thus only exists in the context of open quantum systems. Equilibrium-connected phase transitions are ones which recover the equilibrium transition of a model in the limit of vanishing dissipation. We consider a PT -symmetric Lipkin-Msekov-Glick (LMG) dimer. Each part of the model is individually well understood and we can gain insight by understanding how they are affected by each other. The presence of the environment causes corrections to the critical threshold of the second-order phase transition of the LMG model. We further find that presence of the second-order phase transition delays the PT -phase transition as the system is first driven through various intermediate phases. Quantum systems in general, and open quantum systems in particular suffer exponential scaling of the state space in system size. This makes approximative methods a necessity for the study of strongly-correlated systems. In the second part of the thesis we propose a novel Neural Quantum State (NQS) ansatz for the steady state density matrix. NQS are ansatz functions for variational Monte Carlo whose structure is informed by the architecture of neural networks. A simple NQS is the Restricted Boltzmann Machine (RBM). NQS and in particular RBMs have been shown to possess a volume-law entanglement capacity which significantly expands the range of states NQS can represent over comparable ansatze such as tensor networks. This makes them prime candidates for the representation of highly correlated states of spatially extended systems. The proposed ansatz uses the Choi Isomorphism to represent a local density matrix as a state vector. This allows a simple extension of the basic RBM architecture to represent the state without requiring a complex purification. The ansatz is compared to other approach on two different dissipative transverse field Ising models. We find that the proposed ansatz can more efficiently represent strongly correlated states than competing approaches.
- Advisor / supervisor
- Kirton, Peter
- Resource Type
- DOI
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PDF of thesis T17038 | 2024-08-13 | Público | Descargar |