 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10376825
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 12
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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A bstract We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the YangLee edge singularity. While the leading singular behavior is controlled by the YangLee fixed point (= minimal CFT $$ \mathcal{M} $$ M 2 / 5 ), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator $$ T\overline{T} $$ T T ¯ , and we use the universal properties of the $$ T\overline{T} $$ T T ¯ deformation to fix the contributions of higher orders in the corresponding coupling parameter α . Another irrelevant operator we deal with is the descendant L_ 4 $$ \overline{L} $$ L ¯ _ 4 ϕ of the relevant primary ϕ in $$ \mathcal{M} $$ M 2 / 5 . The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analyticmore »

A bstract A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new $$ \mathcal{N} $$ N = 2 superconformal phase. This is holographically dual to a warped AdS 4 × w S 7 solution of Mtheory equipped with a squashed and stretched metric on S 7 . We determine the spectrum of spin2 operators of the cubic deformation at low energies by computing the spectrum of KaluzaKlein (KK) gravitons over the dual AdS 4 solution. We calculate, numerically, the complete graviton spectrum and, analytically, the spectrum of gravitons that belong to short multiplets. We also use group theory to assess the structure of the full KK spectrum, and conclude that $$ \mathcal{N} $$ N = 2 supermultiplets cannot be allocated KK level by KK level. This phenomenon, usually referred to as “space invaders scenario”, is also known to occur for another AdS 4 solution based on a different squashed S 7 .

A bstract Threedimensional $$ \mathcal{N} $$ N = 4 superconformal field theories contain 1d topological sectors consisting of twisted linear combinations of halfBPS local operators that can be inserted anywhere along a line. After a conformal mapping to a round threesphere, the 1d sectors are now defined on a great circle of S 3 . We show that the 1d topological sectors are preserved under the squashing of the sphere. For gauge theories with matter hypermultiplets, we use supersymmetric localization to derive an explicit description of the topological sector associated with the Higgs branch. Furthermore, we find that the dependence of the 1d correlation functions on the squashing parameter b can be removed after appropriate rescalings. One can introduce real mass and FayetIliopolous parameters that, after appropriate rescalings, modify the 1d theory on the squashed sphere precisely as they do on the round sphere. In addition, we also show that when a generic 3d $$ \mathcal{N} $$ N = 4 theory is deformed by real mass parameters, this deformation translates into a universal deformation of the corresponding 1d theory.

Abstract The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for
N molecular orbitals, the gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a twostep lowrank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with$${\mathcal{O}}({N}^{4})$$ $O\left({N}^{4}\right)$ gate complexity in small simulations, which reduces to$${\mathcal{O}}({N}^{3})$$ $O\left({N}^{3}\right)$ gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with$${\mathcal{O}}({N}^{2})$$ $O\left({N}^{2}\right)$ gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have$${\mathcal{O}}({N}^{3})$$ $O\left({N}^{3}\right)$ depth on a linearly connected array, an improvement over the$${\mathcal{O}}({N}^{2})$$ $O\left({N}^{2}\right)$ scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearestneighbor twoqubit gates, consisting of fewer than 10^{5}nonClifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.$${\mathcal{O}}({N}^{3})$$ $O\left({N}^{3}\right)$ 
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