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Full-Text Articles in Physics
Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas
Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas
Dissertations, Theses, and Capstone Projects
This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …
Phase Transitions, Critical Phenomena, And Correlation Functions In The 2d Ising Model And Its Applications To Quantum Dynamics: A Tensor Network Approach, Sankhya Basu
Dissertations, Theses, and Capstone Projects
This thesis explores several aspects of the 2D Ising Model at both real and complex temperatures utilizing tensor network algorithms. We briefly discuss the importance of tensor networks in the context of forming efficient representations of wavefunctions and partition functions for quantum and classical many-body systems respectively, followed by a brief review of the tensor network renormalization algorithms to compute the one point and two point correlation functions. We use the Tensor Renormalization Group (TRG) to study critical phenomena and examine feasibility of accurate estimations of universal critical data for three critical points for three critical points in two dimensions …