Monte Carlo investigations of Dirac and chiral spin liquids. – (Sasank Budaraju / LPT / Thesis). – 25/10/2024, 14H

Thesis defense

Sasank Budaraju, LPT, 3R4 Fermi Seminar room

Abstract:

Quantum Spin Liquids (QSLs) are exotic states of matter characterized by their many-body quantum entanglement and emergent fractionalized excitations, whose low energy physics is described using gauge theories. The experimental realization of QSLs in crystalline materials and their existence as stable ground states in spin models have been fundamental and widely studied questions in condensed matter physics in recent years.

In this thesis, we employ quantum Monte Carlo simulations to investigate two questions related to QSLs in two dimensions: one focused on gapped spin liquids and the other on gapless spin liquids. The first question concerns whether Projected Entangled Pair States (PEPS, a type of Tensor Network) can accurately represent Chiral Spin Liquids (CSL). Questions have been raised due to a no-go theorem preventing free fermion PEPS representations of chiral non-interacting states. We construct fermionic PEPS (fPEPS) approximants of Gutzwiller-projected Chern insulators (a type of CSL), and demonstrate that fPEPS (of finite bond dimension) can capture the correct topological ground-state degeneracy of the CSL. Further, more general fPEPS are optimized to describe the CSL phase of a frustrated Heisenberg antiferromagnet, and the chiral edge modes in the entanglement spectrum are shown to follow the predictions from conformal field theory. Consequently, our work provides additional supporting evidence that PEPS can effectively
represent CSL phases.

The second question focuses on the nature of low-energy excitations in gapless Dirac Spin Liquids (DSLs), which, unlike gapped spin liquids, lack well-defined fractionalized quasiparticle excitations. Since mean-field descriptions of DSLs may not fully capture their behavior, it is crucial to account for gauge fluctuations beyond the mean-field level. Additionally, the stability of DSLs as ground states in frustrated Heisenberg antiferromagnets remains an unsettled question. In this work, we construct variational ansatzes for low-energy excitations of DSLs. Our results indicate that Heisenberg models on triangular and Kagome lattices support gapless monopole and spinon excitations even after Gutzwiller projection. We further demonstrate that the Dirac spin liquid is energetically stable against the formation of chiral spin liquid states generated by multiple monopole insertions. Moreover, we analyze the momentum quantum numbers of the monopoles, comparing the states before and after projection. Finally, we construct flux excitations localized on (pairs of) individual plaquettes. They are gapped in the thermodynamic limit as expected, but surprisingly have comparable (or even lower) energy than the monopoles for small clusters. Through these results, we provide incremental insights in understanding the low energy excitations of U(1) spin liquids in two dimensions.