In these notes I survey geometric aspects of the lowest Landau level wave functions, integer
quantum Hall state and Laughlin states on compact Riemann surfaces. In particular, I review …

From an experimental point of view, quasielectrons and quasiholes play very similar roles in
the fractional quantum Hall effect. Nevertheless, the theoretical description of quasielectrons …

Conformal field theory has recently been applied to derive few-body Hamiltonians whose
ground states are lattice versions of fractional quantum Hall states. The exact lattice models …

Abstract Model wave functions constructed from (1+ 1) D conformal field theory (CFT) have
played a vital role in studying chiral topologically ordered systems. There usually exist …

We study the interfaces between lattice Laughlin states at different fillings. We propose a
class of model wave functions for such systems constructed using conformal field theory. We …

In these notes I survey geometric aspects of the lowest Landau level wave functions, integer
quantum Hall state and Laughlin states on compact Riemann surfaces. In particular, I review …

We construct a family of 1D and 2D long-range SU (2) spin models as parent Hamiltonians
associated with infinite dimensional matrix product states that arise from simple current …

Strong quantum correlations between many particles in low dimensions lead to emergence
of interesting phases of matter. These phases are often studied through the properties of the …

Strong quantum correlations between many particles in low dimensions lead to emergence
of interesting phases of matter. These phases are often studied through the properties of the …

This thesis is devoted to the application of tensor-network methods to problems in quantum
many-body physics in one and two dimensions and in machine learning. In the first part we …