Related papers: Nonexistence and Uniqueness for Pure States of Fer…

Three-parametric family of non-Hermitian but ${\cal PT}-$symmetric six-by-six matrix Hamiltonians $H^{(6)}(x,y,z)$ is considered. The ${\cal PT}-$symmetry remains spontaneously unbroken (i.e., the spectrum of the bound-state energies…

Using a cone-theoretical method, we prove the uniqueness of the ground state for two Bose Hubbard models. The first model is the usual Bose Hubbard model with real hopping coefficients and attractive interactions. The second model is a…

I discuss two types of non-supersymmetric string model constructions that give at low energy exactly the Standard model (SM) with no additional matter/and or gauge group factors. The construction is based on D6 branes intersecting at angles…

We consider bound states at the vortex core of a non-centrosymmetric superconductor. We show that, despite the mixing of singlet and triplet order parameters, zero energy states survive within certain parameter space as in vortices of some…

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological…

Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the…

To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of…

We present rigorous results for the SU($n$) Fermi-Hubbard model on the railroad-trestle lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$)…

We consider Sch\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\Delta +…

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the…

The double-layer electron system with total filling factor $\nu=1/2$ can be regarded as two separate Fermi-liquid-like states with $\nu=1/4$ when the layer separation is sufficiently large and there is no tunneling. The weak tunneling in…

This paper is devoted to the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a…

Using the semiclassical approach to the energy levels of the fermions bound to the vortex core, we found the difference between the states in nonchiral and chiral superconductors, determined by the Berry phase. The bound states of fermions…

For the frustrated two-dimensional $S=1/2$ antiferromagnetic Heisenberg model close to quantum phase transition we consider the singlet ground states retaining both translational and SU(2) symmetry. Besides usually discussed checkerboard,…

We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like e.g., the topology of potential energy sub-manifolds (PES). This topological…

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $\Delta\to 1^+$ so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge…

We prove the existence, uniqueness, and strict positivity of ground states of the possibly massless renormalized Nelson operator under an infrared regularity condition and for Kato decomposable electrostatic potentials fulfilling a binding…

We show that there are not pure $\mathcal{C}^5$ regular y-global Landsberg surfaced. The proof is based on the averaged connection associated with the linear Chern's connection and the classification of irreducibles holonomies of…

We present a detailed discussion of both theoretical and experimental evidence in favour of the existence of states of ``confined coherence'' in metals of sufficiently high anisotropy and with sufficiently strong correlations. The defining…

We argue that there exists a new class of completely smooth 1/8-BPS, three-charge bound state configurations that depend upon arbitrary functions of two variables. These configurations are locally 1/2-BPS objects in that if they form an…