Exact Diagonalization Studies of the Quantum Link and Quantum Dimer Models

Biswas, Saptarshi (2021) Exact Diagonalization Studies of the Quantum Link and Quantum Dimer Models. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Saptarshi Biswas (16MS079)) 16MS079_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (4MB)

Abstract

In this report we focus on some exotic behaviors of a quantum link model (QLM), and a closely related quantum dimer model, determined using exact diagonalization (ED) methods. Quantum link models are a finite dimensional generalization from Wilson's Lattice gauge theory. The gauge fields realized through parallel transporter variables lying on the lattice links are replaced by quantum spin operators. Here we study the abelian quantum link model and consider S = 1=2 spin operators. The QLM is mapped to the very famous Rokhsar-Kivelson quantum dimer model (QDM) of high Tc superconductivity, by introducing a static charge background. Now, in order to facilitate the ED process some notable symmetries of the two models are expounded over. This leads to a convenient choice of close set of commuting operators. With this machinery we move on to demonstrate a quantum phase transition in the QLM justified using symmetry breaking argument. Then our focus turns to analyzing the non-equilibrium dynamical behavior of the QLM and the QDM. The Hamiltonian of the two models can be cast in form: H = Okin + fiOpot, with being an interaction parameter. We justify that these models are non-integrable by matching their level separation statistics with Wigner-Dyson distribution. Motivated by iii the recent discovery of non-ergodic behavior in an experiment with Rydberg atoms, a urry of theoretical works is focused on understanding such behavior in terms of some strongly athermal energy eigenstates (energy eigenstates away from spectrum edges which violate eigenstate thermalization hypothesis) embedded in an otherwise thermal spectrum, which are dubbed quantum many body scars (QMBS). Much of the theoretical venture that has been taken place revolves around many-body systems furnishing constrained dynamics. Lattice gauge theories provide an archetypal framework for such constrained systems. Therefore, we turn our attention tying to find such athermal states in the energy spectrum of QDM and QLM. Our investigation is based on searching simultaneous eigenstates of Okin and Opot corresponding to the two models, which also provides a unique mechanism of generating such scars. Finally, evidences have been given to justify the athermal nature of these scar states.

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