Related papers: Jaeger's Higman-Sims state model and the B_2 spide…
This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses that arise naturally in the study…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We study a class of subdivision invariant lattice models based on the gauge group $Z_{p}$, with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the $1$- and…
We presents the results of an extensive numerical study of the phase diagram of the spin-1/2, \protect{$J_1$-$J_2$-$J_3$} Heisenberg model on a square lattice, for both ferromagnetic and antiferromagnetic nearest-neighbor interactions…
We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by…
Exact diagonalizations of the spin-1/2 Heisenberg model on the checkerboard lattice have been performed for sizes up to N=36 in the full Hilbert space and N=40 in the restricted subspace of first neighbor dimers. This antiferromagnet does…
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in $S^3$. They contain the same information as the…
In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network;…
We study the spin excitation spectra of the two-dimensional spin-$1/2$ Heisenberg model with a checkerboard structures using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo…
As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…
Given a tied link $L$, the invariant $\langle\langle\cdot\rangle\rangle$ generalizes the Kauffman bracket of classical links. However, the analogues of Kauffman states and their relationship to this invariant are not immediately clear. We…
There are two oriented 4-valent graphical models for the Kauffman polynomial: one (HJ) is obtained by combining Jaeger's formula and Kauffman-Vogel model for the Homflypt polynomial; the other (WF) is obtained by combining Kauffman-Vogel…
We investigate integrable fermionic models within the scheme of the graded Quantum Inverse Scattering Method, and prove that any symmetry imposed on the solution of the Yang-Baxter Equation reflects on the constants of motion of the model;…
We study the Hamiltonian formulation of SU(2) Yang-Mills theory with staggered fermions in a (2+1)-dimensional small lattice system. We construct a gauge-invariant and finite-dimensional Hilbert space for the theory by applying the…
The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. In this…
We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum…
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
The Bose-Hubbard Hamiltonian can be simplified to have only two lattice sites, in which case the system being described is referred to as a dimer. Due to its structure, the hopping term of the dimer Hamiltonian enjoys invariance in a family…