Related papers: A refined Razumov-Stroganov conjecture
We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over $\mathbb{Z},$ and discuss alternatives to the Ozsv\'ath-Szab\'o $\tau$…
Motzkin chain is a model of nearest-neighbor interacting quantum $s=1$ spins with open boundary conditions. It is known that it has a unique ground state which can be viewed as a sum of Motzkin paths. We consider the case of periodic…
This paper constructs coherent states for spin networks with planar symmetry. After gauge-fixing, the full SU(2) symmetry is broken to U(1), but one cannot simply use the U(1) limit of SU(2) coherent states, because the planar states…
The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed of two spins ($\rho, \sigma$) has been presented in detail. The Hamiltonian is not necessarily translational invariant and the exchange…
Charge and spin orderings are studied on the simplest 1D and the 2D square lattice within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagrams method (RPDM)…
A characteristic polynomial is an important invariant in the field of hyperplane arrangement. For the Linial arrangement of any irreducible root system, Postnikov and Stanley conjectured that all roots of the characteristic polynomial have…
We show the existence of an exact ground state in certain parameter regimes of one-dimensional half-filled extended Hubbard model with site-off-diagonal interactions. In this ground state, the bond-located spin correlation exhibits a…
We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign matrices. In addition to those occurring in the O($n=1$)…
We considered a spin chain with nearest neighbor and next nearest neighbor exchange interactions, anisotropic exchange interaction and Dzyaloshinskii-Moriya interaction. The conditions of the spiral spin state as the ground state were…
We have found the exact groundstate for a large class of antiferromagnetic spin-1 models with nearest-neighbour interactions on a linear chain. All groundstate properties can be calculated. The groundstate is determined as a matrix product…
We explore how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. We demonstrate that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike…
We propose a macroscopic description of the superconducting state in presence of an applied external magnetic field in terms of first order differential equations. They describe a corrugated two-component order parameter intertwined with a…
We study Rokhsar-Kivelson (RK) dimer and spin ice models realizing $U(1)$-lattice gauge theories in a wide class of quasi-one-dimensional settings, which define a setup for the study of few quantum strings (closed electric field lines)…
In this paper we settle a weak version of a conjecture (i.e. Conjecture 6) by Mills, Robbins and Rumsey in the paper "Self-complementary totally symmetric plane partitions" (J. Combin. Theory Ser. A 42, 277-292). In other words we show that…
We present a new method to study the ground state of quantum spin systems using the Monte Carlo techniques together with restructured intermediate states which we proposed previously. Our basic idea is to obtain coefficients in the…
We study the enumerative geometry of stable maps to Calabi-Yau 5-folds $Z$ with a group action preserving the Calabi-Yau form. In the central case $Z=X \times \mathbb{C}^2$, where $X$ is a Calabi-Yau 3-fold with a group action scaling the…
New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures are based on the analysis of the ground state of the…
Since the alternating sign matrix conjecture, proposed by Mills, Robbins, and Rumsey in 1982, was proved by Zeilberger and Kuperberg, several refined enumerations have been considered. In particular, Behrend et al. obtained a quadruply…
We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…
We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincare polynomial, and Tutte polynomial. We consider basic algebraic…