Tensor-network representation of gapless frustration-free free fermions
Project Description
Frustration freeness refers to the existence of a ground state which simultaneously minimizes the energy of all the local terms in a Hamiltonian. Such ground states are naturally amenable to a tensor-network representation. In this project, we study how the tensor network representation captures the physical properties of a free-fermion system when the model is frustration free and gapless.
Supervisor
PO, Hoi Chun
Quota
3
Course type
UROP1100
Applicant's Roles
To theoretically and numerically construct tensor-network representation of the relevant free-fermion states and analyze their physical properties.
Applicant's Learning Objectives
- To acquire basic mastery on solid state physics like quantum mechanics in the second quantized form and tight-binding models
- To appreciate with how two-point correlation functions capture all physical observables in a Gaussian state
- To become familiar with how real-space representation could offer an alternative framework for describing quantum many-body states
- To appreciate with how two-point correlation functions capture all physical observables in a Gaussian state
- To become familiar with how real-space representation could offer an alternative framework for describing quantum many-body states
Complexity of the project
Challenging