2025 Theses Doctoral

Exploring Quantum Many-Body Physics with Computational Methods

Zang, Jiawei

This thesis presents an investigation into quantum many-body systems using both theoretical and innovative computational techniques. It has two parts: an investigation of a new class of materials using established methods, and the development of a new set of methods.

First, we use Hartree-Fock calculation to study the moiré Hubbard model that represents the low energy physics of twisted WSe₂ and related materials. In these materials, interaction strength, carrier concentration, and band structure can be controlled by the twist angle and gate voltage. A notable feature is the tunable displacement field, i.e., the gate voltage difference between two layers, leading to a highly tunable van Hove singularity. We calculate the magnetic and metal-insulator phase diagrams and find a reentrant metal-insulator transition controlled by the displacement field. Experimental results for devices with twist angle ∼ 4-5° indicate a similar reentrance, placing these devices in the intermediate coupling regime.

Building on this, the next chapter employs dynamical mean field theory (DMFT) to study the moiré Hubbard model, extending our analysis to include temperature-dependent transport behaviors and phase transitions. We observe that the cube-root van Hove singularity 𝜌(𝜀) ∼ |𝜀|⁻¹/³ contributes to strange metal behavior, characterized by a linear temperature-dependent scattering rate and 𝜔/𝑇 scaling. We compare the results to the experimental findings in twisted homobilayer WSe₂ and heterobilayer MoTe₂ /WSe₂. We find that in twisted WSe₂, the continuous metal-insulator transition is driven by a magnetic transition associated with a change of the displacement field that brings the high order van Hove point of degree three to the Fermi level. The proximity to this van Hove point also induces a linear resistivity. In MoTe₂/WSe₂, one has a paramagnetic metal to paramagnetic Mott insulator transition driven by variation of the bandwidth, with the displacement field effects being unimportant.

In the third study we use the example of magic angle twisted bilayer graphene (TBG) to study the interplay between correlation and band topology. We construct the Wannier basis for TBG involving two triangular site-centered Wannier functions per unit cell derived from the two flat bands per spin per valley. The two crucial point symmetries 𝐶₂𝑇 and 𝐶₃ act locally on the Wannier functions. The Wannier functions have a power-law tail indicative of topological obstruction, but are mostly localized with most charge density concentrated within a single unit cell. This localization significantly enhances the on-site Coulomb interactions relative to interactions with further neighbors, allowing for more accurate estimation of Hamiltonian parameters using a limited set of Wannier functions. Using DMFT, we show that a mixed position/ momentum space representation can be employed, in which the kinetic energy is expressed in the momentum space basis of non-interacting eigenstates, so that all the topological features are exact and well preserved, while the interaction part may be expressed in position space and inherit convenient locality and symmetry properties from the Wannier functions.

Finally, we introduce a novel, data-driven approach to compress the two-particle vertex function. Using PCA and an autoencoder neural network, we achieve significant reductions in complexity while maintaining high fidelity in representing the underlying physics. We demonstrate that a linear PCA not only provides deeper physical insights but also exhibits superior zero-shot generalization compared to more complex nonlinear models. Further, we explore the relationships between different quantum states by identifying principal component subspaces common across known phases. Our analysis reveals that while the vertex functions necessary for describing ferromagnetic states differ significantly from those describing the Fermi liquid state, those required for antiferromagnetic and superconducting states share a common foundation, hinting at their emergence from pre-existing fluctuations in the Fermi liquid state.