This series consists of talks in the area of Quantum Matter.
We present our recent numerical calculations for the Heisenberg model on the square and
Kagome lattices, showing that gapless spin liquids may be stabilized in highly-frustrated
regimes. In particular, we start from Gutzwiller-projected fermionic states that may
describe magnetically disordered phases,[1] and apply few Lanczos steps in order to improve
their accuracy. Thanks to the variance extrapolation technique,[2] accurate estimations of
the energies are possible, for both the ground state and few low-energy excitations.
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at fillings 8 and 12 with experimentally-testable consequences. We also show examples for Abelian fractional quantum Hall states, the simplest examples being at filling fractions 8/7, 12/11, 8/15, 16/5. For all examples, we propose experiments that can distinguish distinct edge phases. Our results are summarized by the observation that edge phases correspond to lattices while bulk phases correspond to genera of lattices.
We review the formalism of matrix product states and one of its recent generalisations which allows to variationally determine the dispersion relation of elementary excitations in generic one-dimensional quantum spin chains. These elementary excitations dominate the low energy effective behaviour of the system. We discuss recent work where we show how we can also describe the effective interaction between these excitations – as mediated by the strongly correlated ground state – and how we can extract the corresponding S matrix.
Electron puddles created by doping of a 2D topological insulator may violate the ideal helical edge conductance. Because of a long electron dwelling time, even a single puddle may lead to a significant inelastic backscattering. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on temperature and on the doping level. Puddles with odd electron number carry a spin and lead to a logarithmically-weak temperature dependence of the resistivity of a long edge.
In the first part of the seminar, I will describe a general approach to write down a large family of model SU(N) anti-ferromagnets that do not suffer from the sign problem. In the second half I will show how such Hamiltonians are useful for the study of deconfined quantum critical points and possibly other exotic physics.
Quantum Monte Carlo is a versatile tool for studying strongly interacting theories in condensed matter physics from first principles. A prominent example is the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. I will present numerical results for different properties of the homogeneous, spin-balanced unitary Fermi gas across the superfluid transition, such as the critical temperature, the equation of state and the temperature dependence of the contact density. Our values show good agreement with recent experimental data.
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this talk, I consider a simple bilayer fractional quantum Hall (FQH) system with the 1/3 Laughlin state in each layer, in the presence of interlayer tunneling.
Superselection rules in quantum theory assert the impossibility of preparing coherent superpositions of certain conserved quantities. For instance, it is commonly presumed that there is a superselection rule for charge and for baryon number, as well as a "univalence superselection rule" forbidding a coherent superposition of a fermion and a boson. I will show how many superselection rules can be effectively lifted using a reference frame for the variable that is conjugate to the conserved quantity.