Condensed Matter

The Kitaev model with anisotropic interactions on the bonds of a honeycomb lattice is a paradigmatic model for quantum spin liquids. Despite the simplicity of the model, a rich phase diagram with gapless and gapped quantum spin liquid phases, with abelian and non-abelian excitations, are revealed as a function of a magnetic field and bond couplings. Our results of the entanglement entropy, topological entanglement entropy, and the dynamical spin excitation spectrum, are obtained using exact diagonalization and density matrix renormalization group (DMRG) methods. We provide insights into the phases from the underlying effective field theories. In collaboration with Shi Feng, Cullen Gantenberg, Adhip Agarwala, Subhro Bhattacharjee [1] Signatures of magnetic-field-driven quantum phase transitions in the entanglement entropy and spin dynamics of the Kitaev honeycomb model, David C. Ronquillo, Adu Vengal, Nandini Trivedi, Phys. Rev. B 99, 140413 (2019) [2] Magnetic field induced intermediate quantum spin-liquid with a spinon Fermi surface, Niravkumar D. Patel and Nandini Trivedi, Proceedings of the National Academy of Sciences 116, 12199 (2019). [3] Two-Magnon Bound States in the Kitaev Model in a [111]-Field, Subhasree Pradhan, Niravkumar D. Patel, Nandini Trivedi, Phys. Rev. B 101, 180401 (2020) [4] Symmetry Analysis of Tensors in the Honeycomb Lattice of Edge-Sharing Octahedra, Franz G. Utermohlen, Nandini Trivedi, Phys. Rev. B 103, 155124 (2021)

Starting from the Villain formulation with an additional constraint we construct a self-dual lattice version of U(1) field theory with a theta-term. An interesting feature is that the self-dual symmetry gives rise to an action that is local but not ultra-local, similar to lattice actions that implement chiral symmetry. We outline how electric and magnetic matter can be coupled in a self-dual way and discuss the emerging symmetry structure with the theta term. We present results from a Monte Carlo simulation of the self-dual system with electric and magnetic matter and explore spontaneous breaking of the self-dual symmetry.

The sign problem is arguably the greatest weakness of the otherwise highly efficient, non-perturbative Monte Carlo simulations. Recently, considerable progress has been made in alleviating the sign problem by deforming the integration contour of the path integral into the complex plane and applying machine learning to find near-optimal alternative contours. This deformation however requires a Jacobian determinant calculation which has a generic computational cost scaling as volume cubed. In this talk I am going to present a new architecture with linear runtime, based on complex-valued affine coupling layers.

 

Unlike conventional global symmetries that act on all of space, subsystem symmetries act only on rigid subspaces such as lines, planes or fractal regions. Such symmetries are of interest for their close connection to fracton physics and in their own right. In this talk, I discuss phenomena that can occur in two-dimensional systems with subsystem symmetry and anyon excitations, where the symmetry fractionalizes on anyon excitations. This turns out to be manifest in the mobility of the fractionalized excitations under dynamics that respect the symmetry. Such symmetry fractionalization was previously thought to be impossible, and indeed there are a number of differences from conventional symmetry fractionalization. I will present a general framework to describe subsystem symmetry fractionalization in two dimensions, and give a number of simple examples of this phenomenon in commuting Pauli Hamiltonians.

This talk is based on arXiv:2203.13244, work in collaboration with David Stephen, Arpit Dua, José Garre-Rubio and Dominic Williamson.

Zoom Link: https://pitp.zoom.us/j/93741883840?pwd=RlMrUGwwVEt5WFdoNGpkMmdSVXp5UT09

We develop a new method for bosonizing the Fermi surface. In this method, a system with a Fermi surface is described as a coadjoint orbit of the group of canonical transformations. The method naturally parametrizes the Fermi surface by a bosonic field that depends on the spacetime coordinates and the position on the Fermi surface. The Wess-Zumino-Witten term in the effective action, governing the adiabatic phase acquired when the Fermi surface changes its shape, is completely fixed by the Kirillov-Kostant-Souriau symplectic form on the coadjoint orbit. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Possible extensions of the theory are described.  Reference: arXiv:2203.05004.

Zoom Link: https://pitp.zoom.us/j/95453440138?pwd=b0Fmbi9HTU9nYTA3Y2F6dWlha294UT09

Magic-angle (θ=1.05∘) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f- and c-electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f-electrons coupled to nearly free topological semimetallic c-electrons - we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations and the minima of the charge gap at the Γ point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG. All the model’s parameters are analytically derived.