This series consists of talks in the area of Condensed Matter.
Quantum many-body systems are challenging to study because of their exponentially large Hilbert spaces, but at the same time they are an area for exciting new physics due to the effects of interactions between particles. For theoretical purposes, it is convenient to know if such systems can be expressed in a simpler way in terms of some nearly-free quasiparticles, or more generally if one can construct a large set of operators that approximately commute with the system’s Hamiltonian. In this talk I will discuss two ways of using the entanglement spectrum to tackle these questions.
One dimensional symmetry protected topological (SPT) phases are gapped phases of matter whose edges are degenerate if the Hamiltonian respects a particular symmetry. With their interacting classification having been understood since 2010, we would like to further our understanding by addressing the following two questions: (1) Is there a unified way of understanding some of the exactly soluble models for 1D SPTs? And (2) if we are given two arbitrary SPTs, can we predict the structure of the phase transition between them? The answers turn out to be surprisingly simple.
Magnetic skyrmions are highly mobile nanoscale topological spin textures. We show, both analytically and numerically, that a magnetic skyrmion of an even azimuthal winding number placed in proximity to an s-wave superconductor hosts a zero-energy Majorana bound state in its core, when the exchange coupling between the itinerant electrons and the skyrmion is strong. This Majorana bound state is stabilized by the presence of a spin-orbit interaction. We propose the use of a superconducting tri-junction to realize non-Abelian statistics of such Majorana bound states.
Strongly interacting quantum systems driven out of equilibrium represent a fascinating field where several questions of fundamental importance remains to be addressed [1].
These range from the dynamics of high-dimensional interacting models to the thermalization properties of quantum gases in continuous space.
In this Seminar I will review our recent contributions to some of the dynamical quantum problems which have been traditionally inaccessible to accurate many-body techniques.
Tensor networks have been very successful for approximating quantum states that would otherwise require exponentially many parameters.
I will discuss how a similar compression can be achieved in models used to machine learn data, such as sets of images, by representing the fitting parameters as a tensor network. The resulting model achieves state-of-the-art performance on standard classification tasks. I will discuss implications for machine learning research, exploring which insights from physics could be imported into this field.
I will discuss the stability and breakdown of the topological classification of gapped ground states of non-interacting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions. In our approach [1], the effects of interactions on the boundary gapless modes are encoded in terms of boundary dynamical masses. Breakdown of the non-interacting topological classification occurs when the quantum nonlinear sigma models for the boundary dynamical masses favor quantum disordered phases.
I will review recent progress on theory of many-body localization, mostly focusing on properties of the many-body localized phase itself.
I will discuss explicit construction of effective Hamiltonians governing the dynamics of conserved quantities. The analysis reveals several inequivalent length scales in the system, some of which do not appear to diverge on the approach to the thermalized phase.
Experimental protocols to measure these length scales will also be discussed.
Numerical results suggest that the quantum Hall effect at {\nu} = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at {\nu} =
We numerically investigate the expansion of clouds of hard-core bosons in a 2D square lattice using a matrix-product state based method. This non-equilibrium setup is induced by quenching a trapping potential to zero and is specifically motivated by an experiment with ultracold atoms [1]. As the anisotropy for hopping amplitudes in different spatial directions is varied from 1D to 2D, we observe a crossover from a fast ballistic expansion in the 1D limit to much slower dynamics in the isotropic 2D lattice [2].