correlation effects in topological phase transitions

Tieyan Si

Francesca Paoletti

This thesis focuses on the effects of strong electron-electron interactions on topological phase transitions.In very general terms, topological phase transitions are typically associated with the formation of gapless states at the boundary between two gapped phases.The opening of a gap is usually associated with a spontaneous symmetry breaking that can obliterate the topological nature of the system.In this work we highlight a completely different destiny for a topological transition in the presence of interaction and we develop a theoretical framework to address this physics identifying the physical origin for the unconventional scenario.In particular, we show that strong electronic correlation can lead to a gap opening at the topological transition without any symmetry breaking.This turns the topological transition discontinuous, thereby giving rise to a quantum critical point connecting the continuous region with the discontinuous one.This unconventional scenario establishes a surprising connection between a topological transition and quantum criticality.By solving a Bernevig-Hughes-Zhang model supplemented with a local symmetric interaction, we demonstrate that the crucial role of orbital polarization naturally emerges, already at the mean-field level.This local parameter effectively captures the essence of the topological transition, complementing the established evaluation of topological invariants and enabling a Landau-like description.Within this framework, we analyze the interplay between band topology and the dynamical effects of electronic correlations, achieved by developing a non-perturbative method for calculating the effective free energy, the Variational Gaussian Approximation, which is compared with both a simple static mean-field, which is not able to capture any critical behavior for the topological transition and with the accurate Dynamical Mean-Field Theory which provides an important benchmark for the accuracy of the approach.We show indeed that dynamical quantum fluctuations can lead to gap opening without any symmetry breaking.The growth of these quantum effects as the interaction is increased turns indeed the topological transition from continuous to discontinuous.This change of behavior is associated with the presence of massive Dirac fermion at the transition point showing a Gross-Neveu critical behaviour near the quantum critical endpoint.We identify the gap opening as a condensed matter analog of the Coleman-Weinberg mechanism of mass generation.The theory presented offers a broad scope for extension in various directions, ranging from changing the topological model and modifying the interactions, to incorporating non-local effects, or even applying it to entirely trivial strongly correlated models.

M. A. Contínentino

Robert-Jan Slager

Jun-Hui Zheng, Arijit Dutta, Monika Aidelsburger +1 more

The impact of weak disorder and its spatial correlation on the topology of a Floquet system is not well understood so far. In this study, we investigate a model closely related to a two-dimensional Floquet system that has been realized in experiments. In the absence of disorder, we determine the phase diagram and identify an exotic phase characterized by edge states with alternating chirality in adjacent gaps. When weak disorder is introduced, we examine the disorder-averaged Bott index and analyze why the anomalous Floquet topological insulator is favored by both uncorrelated and correlated disorder, with the latter having a stronger effect. For a system with a ring-shaped gap in the energy spectrum, the Born approximation fails to explain the topological phase transition, unlike for a system with a pointlike gap.

Jason C. Pillay, Ian P. McCulloch

The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.