We explore how to build quantum circuits that compute the lowest energy state corresponding a given Hamiltonian within symmetry subspace by explicitly encoding it into circuit. create an explicit unitary and variationally trained maps any vector output ansatz A(α→) from defined in space. The parameters are varitionally minimize energy, thus keeping labelled value. method was tested for spin XXZ...

Trapped and cooled gases of alkali atoms can be manipulated to exhibit a variety of interesting phenomena. For example, dilute gases of fermionic atoms, in 2 hyperfine states, can be cooled to temperatures where they become superfluid. An external field can be applied to tune the scattering length a. When |a| exceeds the interparticle spacing, nonperturbative tools are needed to study the syste...

We consider classes of reconstruction systems (RS’s) for finite dimensional real or complex Hilbert spaces H, called group reconstruction systems (GRS’s), that are associated with representations of finite groups G. These GRS’s generalize frames with high degree of symmetry, such as harmonic or geometrically uniform ones. Their canonical dual and canonical Parseval are shown to be GRS’s. We est...

We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are e...

Abstract. The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and perform a multifractal analysis for the eigenstates. From the size and disorder dependence of the variance of the nearest neighbor energy spacing ...

I review the relationship between AdS/CFT ( anti-de Sitter / conformal field theory) dualities and the general theory of unitary lowest weight (ULWR) (positive energy) representations of non-compact space-time groups and supergroups. The ULWR’s have the remarkable property that they can be constructed by tensoring some fundamental ULWR’s ( singletons or doubletons). Furthermore, one can go from...

We consider a spontaneously broken abelian gauge theory with a scalar-fermion coupling non-linear in the Higgs field, which reduces to a Yukawa term in the unitary gauge. We examine in this gauge the one-loop divergences in a physical process and we find they are not all of the renormalizable type. Comparison is made with the linear coupling theory, where cancellation of the non-renormalizable ...

We have carried a theoretical study of the Kp → MBγ reaction with MB = Kp, K̄0n, π−Σ+, π+Σ−, π0Σ0, π0Λ, for K lab. momenta between 200 and 500 MeV/c, using a chiral unitary approach for the strong Kp interaction with its coupled channels. The Λ(1405) resonance, which is generated dynamically in this approach, shows up clearly in the dσ/dMI spectrum, providing new tests for chiral symmetry and th...

Flat bands have band crossing points with other dispersive in many systems including the canonical flat models Lieb and kagome lattices. Here we show that some of such degeneracy are unavoidable because symmetry representation (SR) under unitary symmetry. We refer to a point as SR-enforced crossing. is distinct from conventional protected by eigenvalues or topological charges its protection req...