Related papers: Extended quantum U(1)-liquid phase in a three-dime…
The $\mathbb{Z}_2$ topological phase in the quantum dimer model on the Kagom\'e-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the…
Quantum electrodynamics in $2+1$ dimensions (QED$_3$) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional…
Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in…
We study a model of strongly correlated S=1/2 fermions on the planar pyrochlore, or checkerboard, lattice, at fractional (1/8) filling. Starting with the extended Hubbard model in the limit of strong Coulomb repulsion, low-energy…
We investigate the Kagome lattice Hubbard model at half-filling by variational Monte-Carlo with testing the U(1)-Dirac spin liquid, uniform and valence bond crystal states. Even for the large-$U$ case the U(1) Dirac state, being the optimal…
Quantum phase transitions from the cluster-charge interaction, which is composed of competing short- and long-range interactions, are investigated on a $\pi$-flux lattice by using the mean-field theory and determinant quantum Monte Carlo…
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a…
Quantum dimer models typically arise in various low energy theories like those of frustrated antiferromagnets. We introduce a quantum dimer model on the kagome lattice which stabilizes an alternative $\mathbb{Z}_2$ topological order, namely…
In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. With this formulation of the Kondo lattice, we study a spin chain coupled to two-dimensional Dirac conduction electrons. The spin…
We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte-Carlo simulations. This system has two quantum phase transitions, a generic one for small…
The extended Hubbard model (EHM) describes fermions on a lattice coupled through on-site, $U$, and first-neighbor, $V$, interactions. In the context of high-$T_c$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel,…
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in…
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice exhibits an intriguing temperature-driven phase transition in a magnetic field between a classical ferrimagnetic phase and a quantum monomer-dimer phase. A…
We report recent analytical progress in the quest for spin models realising exotic phases. We focus on the question of `reverse-engineering' a local, SU(2) invariant S=1/2 Hamiltonian to exhibit phases predicted on the basis of effective…
We propose a general construction of commuting projector lattice models for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The construction starts from a commuting projector model of…
The nature and the very existence of the resonant plaquette valence bond state that separates the classical columnar phase and the Rokhsar and Kivelson point in the quantum dimer model remains unsettled. Here we take a different line of…
The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light--matter coupling strength. Extending this model by…
We study the ground-state properties of a system of dimers. Each dimer consists in a pair of equivalent charges at a fixed distance, immersed in a neutralizing homogeneous background. All charges interact pairwisely by Coulomb potential.…
Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…