Dynamical Signatures of Strongly Correlated Topological Phases of Matter
Final Report Abstract
The goal of this project was to find dynamical signatures that allow for the identification of strongly correlated topological phases of matter. These phases are collective quantum states of particles in two dimensions at absolute zero temperature which repel each other strongly and the phases have properties that are very robust to external perturbations. These states are both of fundamental scientific interest and might be useful for fault-protected quantum information processing. In particular, I investigated so-called fractional Chern insulators that could be realized in optical lattices of ultracold atoms, atoms that are trapped by laser light in a periodic array and can move within this array. I theoretically studied how these states evolve in time after local and global perturbations and whether this dymamical behavior is suitable to identify the state in possible experiments. In the case of local perturbations, we showed that the state can be distinguished from a different weakly interacting version by its chiral response, i.e. the preference of particles moving in clockwise direction as opposed to counterclockwise, or vice-versa. For the scenario of a global perturbation, we demonstrated that one of the hallmark properties of the state, its Hall conductivity, can be determined from the movement of particles in an experimentally realistic setup. The Hall conductivity quantifies the the motion of particles into a direction when applying a force that points into the perpendicular direction. In the case of fractional Chern insulators, it has a uniquely quantized value that allows the unabmbiguous identification of the phase. Investigating these two main goals of the project still left time for additional research which is partly related. We showed that a similar magnetic version of a fractional Chern insulator, a chiral spin liquid, is surprisingly occurring in a different theoretical model, the Hubbard model on the triangular lattice. This is a quintessential model of condensed matter physics and the nature of the state in this parameter regime had been under debate for several decades. Relating to the original proposal, this might be a state that is more suitable to experimental detection in optical lattices since its realization is less prone to heating effects that would destroy the state after a certain time or in the worst case prevent its formation altogether. However, the occurence of this state is not limited to optical lattices since a similar theoretical description applies to several materials. This opens several routes to the possible experimental observation of the chiral spin liquid three and a half decades after its prediction. On the theoretical side, we found an explanation for the mechanism that governs the appearance of the chiral spin liquid, a knowledge that can help to identify candidate models and materials that host similar states. Finally, we demonstrated that there is an alternative algorithm to the one that was used to obtain a large part of the results in the project, which is more reliable in specific different situations.
Publications
- Charge Excitation Dynamics in Bosonic Fractional Chern Insulators, Phys. Rev. Lett. 121, 086401 (2018)
X.-Y. Dong, A. G. Grushin, J. Motruk, and F. Pollmann
(See online at https://doi.org/10.1103/PhysRevLett.121.086401) - Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study, Phys. Rev. X 10, 021042 (2020)
A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore
(See online at https://doi.org/10.1103/PhysRevX.10.021042) - Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement, Phys. Rev. Lett. 125, 236401 (2020)
J. Motruk and I. Na
(See online at https://doi.org/10.1103/PhysRevLett.125.236401) - Performance of the rigorous renormalization group for first-order phase transitions and topological phases, Phys. Rev. B 103, 195122 (2021)
M. Block, J. Motruk, S. Gazit, M. P. Zaletel, Z. Landau, U. Vazirani, and N. Y. Yao
(See online at https://doi.org/10.1103/PhysRevB.103.195122) - Phase diagram of the anisotropic triangular lattice Hubbard model, Phys. Rev. B 103, 235132 (2021)
A. Szasz and J. Motruk
(See online at https://doi.org/10.1103/PhysRevB.103.235132)
