Related papers: Physical Combinatorics and Quasiparticles
The Z_k parafermionic conformal field theories, despite the relative complexity of their modes algebra, offer the simplest context for the study of the bases of states and their different combinatorial representations. Three bases are…
We introduce a fermionic formula associated with any quantum affine algebra U_q(X^{(r)}_N). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to…
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in…
We study the dynamical behaviour of ultracold fermionic atoms loaded into an optical lattice under the presence of an effective magnetic flux, induced by spin-orbit coupled laser driving. At half filling, the resulting system can emulate a…
We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations…
A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…
We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…
Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. The lectures start with basic considerations on energy scales, and on the regimes in which a…
The W-infinity minimal models are conformal field theories which can describe the edge excitations of the hierarchical plateaus in the quantum Hall effect. In this paper, these models are described in very explicit terms by using a bosonic…
We consider the RSOS S-matrices of the Phi(1,5) perturbed minimal models which have recently been found in the companion paper [hep-th/9604098]. These S-matrices have some interesting properties, in particular, unitarity may be broken in a…
We study some sorts of dimensionally-deconstructed models for supersymmetric (Euclidean) quantum mechanics, or zero-dimensional field theory. In these models, we assign bosonic and fermionic variables to vertices and edges of a graph. We…
The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level $k$ integrable highest weight $U_q(\widehat{sl_2})$ modules in terms of the creation operators at…
Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle…
We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for…
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role…
We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of…
We calculate the properties of a one-dimensional $Z_2$ lattice gauge theory in different Gauss law sectors, corresponding to different configurations of static charges set by the orientations of the gauge spins. Importantly, in quantum…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
We revisit various topological issues concerning four-dimensional ungauged and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum chromodynamics (QCD), from the modern bordism point of view. We explain, for example, why the…
We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFT's possess perturbations which define integrable QFT's. We establish that these QFT's have local and…