Related papers: Phase diagram for hard-core $\mathbb{Z}_3$ anyons …
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study…
We study the phase structure of a three dimensional Abelian Higgs model with singly- and doubly-charged scalar fields coupled to a compact Abelian gauge field. The model is pretending to describe systems of strongly correlated electrons…
We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In…
In presence of a strong external magnetic field the dynamics of solitons in a one-dimensional easy-plane Heisenberg antiferromagnet exhibits a number of peculiarities. Dynamics of internal soliton degrees of freedom is essentially quantum,…
The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to…
We study a one-dimensional system of strongly interacting anyons with short-range interactions under external confinement. This system, referred to as $p$-wave anyons, interpolates continuously between spin-polarized fermions with $p$-wave…
Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field (Atala et al., Nature Physics \textbf{10}, 588 (2014)), we study the dynamics of bosons on a tight-binding two-leg…
Quantum particle statistics fundamentally controls the way particles interact, and plays an essential role in determining the properties of the system at low temperature. Here we study how the quantum statistics affects the computational…
The series of articles [Ann. Phys. 345, 73 (2014) and 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with $f=2$ degrees of freedom is continued by studying the interacting boson model of nuclear…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects…
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has…
Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin…
Recent measurements on 2d materials tuning between fractional quantum anomalous Hall phases and a plethora of correlated electronic states call for a detailed understanding of the dynamics of anyons. Here we develop a general theory of the…
While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the…
The algebraic tools used to study topological phases of matter are not clearly suited to studying processes in which the bulk energy gap closes, such as phase transitions. We describe an elementary two edge thought experiment which reveals…
We study an exactly solvable model of $D(D_3)$ non-Abelian anyons on a one-dimensional lattice with a free coupling parameter in the Hamiltonian. For certain values of the coupling parameter level crossings occur, which divide the…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
Anyons, quasiparticles living in two-dimensional spaces with exotic exchange statistics, can serve as the fundamental units for fault-tolerant quantum computation. However, experimentally demonstrating anyonic statistics is a challenge due…
We investigate the dynamics of a gas of non-interacting particle-like soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by…