Condensed Matter

When the wavefunction of a macroscopic system unitarily evolves from a low-entropy initial state, there is good circumstantial evidence it develops "branches", i.e., a decomposition into orthogonal components that can't be distinguished from the corresponding incoherent mixture by feasible observations, with each component a simultaneous eigenstate of preferred macroscopic observables.  Is this decomposition unique?  Can the number of branches decrease in time?

Answering these questions is hard because branches are defined only intuitively, much like early investigations of algorithms prior to the Church–Turing thesis.  A rigorous definition could give a speed up to certain non-stationary matrix-product state numerical simulations, as well as solve Kent's Set Selection problem in the consistent histories formalism, a 20-year-old open challenge in the foundations of quantum mechanics. I introduce some tentative definitions based on the idea of redundant information, and establishing a uniqueness theorems. A key counterexample is provided by the Shor error-correction code, which demonstrates that branch structure with robust, redundant records on macroscopic scales can hide incompatible (noncommuting) structure on microscopic scales.

We consider d=2 fermions at finite density coupled to a critical boson. In the quenched or Bloch-Nordsieck approximation, where one takes the limit of fermion flavors N_f→0, the fermion spectral function can be determined {exactly}. We show that one can obtain this non-perturbative answer thanks to a specific identity of fermionic two-point functions in the planar local patch approximation. The resulting spectrum is that of a non-Fermi liquid: quasiparticles are not part of the exact fermionic excitation spectrum of the theory. Instead one finds continuous spectral weight with power law scaling excitations. Moreover, at low energies there are three such excitations at three different Fermi surfaces, two with a low energy Green's function G∼(ω−v k)^−1/2 and one with G∼|ω+k|^−1/3. We proceed to study this model with a finite N_f but still neglecting fermionic loops with 3 or more vertices, motivated by multiloop cancellations at large k_F. We still find a non-Fermi liquid but with a different IR spectrum.

Experimentalists have recently been able to engineer non-trivial topological band structures using ultracold atoms in optical lattices.

Motivated by ongoing experimental efforts to tune interactions, we explore the interplay between strong correlations and topology in these systems. Focusing on the Haldane-Hubbard honeycomb model as an example, we show that its strongly interacting Mott limit exhibits various chiral magnetic orders, including a wide regime of triple-Q tetrahedral order. Incorporating an additional third-neighbour hopping frustrates and ultimately "quantum-melts" the tetrahedral magnetic order. From analysing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations. Our numerical results suggest that this frustration induced melting may be realised as an exotic continuous quantum phase transition. Finally, we discuss recent results which point toward a common mechanism of realising chiral spin liquids through the continuous melting of non-coplanar magnetic "parent" states.

Incommensurate charge order is a phenomenon in which the electrons in a crystal attempt to order with a period irrationally-related to that of

the lattice spacing. In the first half of this talk I will present recent work [1] in which we demonstrate that incommensurately charge-ordered systems can lower their free energy by forming quasicrystals: slices through higher-dimensional crystals with properties lying between  periodicity and disorder. The result potentially greatly increases the number of known, naturally-occuring quasicrystals from the two present examples, both of which were found in the same Siberian meteorite. In the second half I will present work from an ongoing experimental collaboration in which atomically-resolved scanning tunneling microscopy and atomic force microscopy on semiconducting monolayers of molybdenum diselenide (MoSe2) see conducting edge states along one-dimensional mirror twin boundaries. Remarkably, these edge states then develop their own energy gap via charge ordering [2]. We see a number of features suggestive of incommensurate order. By employing a simple analytical model we demonstrate that the effect is in fact a result of fine-tuning between charge ordering and quantum well physics coming from the small system size (on the order of thirty atoms).

[1] F. Flicker and Jasper van Wezel, Physical Review Letters 115, 236401

(2015), Natural 1D Quasicrystals from Incommensurate Charge Order

[2] S. Barja et al., Nature Physics 12, 751-757 (2016), Charge density

wave order in 1D mirror twin boundaries of single-layer MoSe2