scholarly journals Duality relations for overlaps of integrable boundary states in AdS/dCFT

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Charlotte Kristjansen ◽  
Dennis Müller ◽  
Konstantin Zarembo
Keyword(s):  
Spin Chain ◽  
Universal Formula ◽  
System Calls ◽  
Bethe Root ◽  
Duality Relations ◽  
Boundary States ◽  
Significant Step ◽  
Bethe Equations

Abstract The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a universal formula in the case of overlaps between Bethe eigenstates and integrable boundary states, of relevance for AdS/dCFT, by determining the transformation properties of the overlaps under fermionic as well as bosonic dualities which allows us to move between any two descriptions of the spin chain encoded in the QQ-system. An important part of our analysis involves introducing a suitable regularization for singular Bethe root configurations.

scholarly journals A universal formula for avian egg shape

2020 ◽  
Author(s):  
Valeriy G. Narushin ◽  
Michael N. Romanov ◽  
Darren K. Griffin
Keyword(s):  
Mathematical Model ◽  
Mathematical Formulation ◽  
Additional Function ◽  
Geometric Figures ◽  
Universal Formula ◽  
Egg Shape ◽  
Significant Step ◽  
Last Stage ◽  
Pointed End ◽  
Avian Egg

AbstractThe bird’s oomorphology has far escaped mathematical formulation universally applicable. All bird egg shapes can be laid in four basic geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical/pear-shaped). The first three have a clear mathematical definition, each derived from expression of the previous, but a formula for the pyriform profile has yet to be inferred. To rectify this, we introduced an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere—ellipsoid—Hügelschäffer’s ovoid transformation applicable to any avian egg shape geometry. Required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical description is invariably a significant step in understanding not only the egg shape itself, but how and why it evolved, thus making widespread biological and technological applications theoretically possible.

scholarly journals Overlaps and fermionic dualities for integrable super spin chains

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Charlotte Kristjansen ◽  
Dennis Müller ◽  
Konstantin Zarembo
Keyword(s):  
Lie Algebras ◽  
Spin Chain ◽  
Dynkin Diagram ◽  
Symmetry Algebra ◽  
Spin Chains ◽  
Dynkin Diagrams ◽  
Boundary States ◽  
The One

Abstract The $$ \mathfrak{psu}\left(2,\left.2\right|4\right) $$ psu 2 2 4 integrable super spin chain underlying the AdS/CFT correspondence has integrable boundary states which describe set-ups where k D3-branes get dissolved in a probe D5-brane. Overlaps between Bethe eigenstates and these boundary states encode the one-point functions of conformal operators and are expressed in terms of the superdeterminant of the Gaudin matrix that in turn depends on the Dynkin diagram of the symmetry algebra. The different possible Dynkin diagrams of super Lie algebras are related via fermionic dualities and we determine how overlap formulae transform under these dualities. As an application we show how to consistently move between overlap formulae obtained for k = 1 from different Dynkin diagrams.

scholarly journals Integrable boundary states in D3-D5 dCFT: beyond scalars

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Charlotte Kristjansen ◽  
Dennis Müller ◽  
Konstantin Zarembo
Keyword(s):  
Perturbation Theory ◽  
Domain Wall ◽  
Gauge Group ◽  
Spin Chain ◽  
Boundary State ◽  
Boundary States ◽  
Local Operators ◽  
Set Up ◽  
The One

Abstract A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the gauge group jumps by k units across a domain wall. The one-point functions of local operators in this set-up map to overlaps between on-shell Bethe states in the underlying spin chain and a boundary state representing the D5 brane. Focussing on the k = 1 case, we extend the construction to gluonic and fermionic sectors, which was prohibitively difficult for k > 1. As a byproduct, we test an all-loop proposal for the one-point functions in the su(2) sector at the half-wrapping order of perturbation theory.

scholarly journals Preparing exact eigenstates of the open XXZ chain on a quantum computer

2021 ◽  
Author(s):  
John S. Van Dyke ◽  
Edwin Barnes ◽  
Sophia Economou ◽  
Rafael I Nepomechie
Keyword(s):  
Spin Chain ◽  
Quantum Computer ◽  
Success Probability ◽  
Integrable Model ◽  
Quantum Algorithm ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Real Solutions ◽  
Xxz Chain ◽  
Bethe Equations

Abstract The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of (L M) 2M M! terms, the algorithm requires L + M2+ 2M qubits.

scholarly journals Root patterns and energy spectra of quantum integrable systems without U(1) symmetry: the antiperiodic XXZ spin chain

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Xiong Le ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kangjie Shi ◽  
...  
Keyword(s):  
Physical Properties ◽  
Thermodynamic Limit ◽  
Spin Chain ◽  
State Energy ◽  
Integrable Models ◽  
Analytic Method ◽  
Quantum Integrable Systems ◽  
Bethe Root ◽  
Quantum Integrable Models ◽  
Universal Procedure

Abstract Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without U(1) symmetry, their spectra are usually given by inhomogeneous T − Q relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic XXZ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.

scholarly journals Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots

2021 ◽  
Author(s):  
Nikolai Kitanine ◽  
◽  
Giridhar Kulkarni ◽  
◽  
◽  
...  
Keyword(s):  
Bethe Ansatz ◽  
Thermodynamic Limit ◽  
Spin Chain ◽  
Form Factors ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Bethe Equations ◽  
Treat All ◽  
Ansatz Approach

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.

ctDNA as a prognostic factor in operable colon cancer patients: a systematic review and meta-analysis

2020 ◽  
Author(s):  
Emre Yekedüz ◽  
Elif Berna Köksoy ◽  
Hakan Akbulut ◽  
Yüksel Ürün ◽  
Güngör Utkan
Keyword(s):  
Colon Cancer ◽  
Prognostic Factor ◽  
Cancer Patients ◽  
Meta Analysis ◽  
Circulating Tumor Dna ◽  
Random Effects Model ◽  
Inverse Variance ◽  
Increased Risk ◽  
Significant Step ◽  
Tumor Dna

Aim: Using circulating tumor DNA (ctDNA) instead of historical clinicopathological factors to select patients for adjuvant chemotherapy (ACT) may reduce inappropriate therapy. Material & methods: MEDLINE was searched on March 31, 2020. Studies, including data related to the prognostic value of ctDNA in the colon cancer patients after surgery and after ACT, were included. The generic inverse-variance method with a random-effects model was used for meta-analysis. Results: Four studies were included for this meta-analysis. ctDNA-positive colon cancer patients after surgery and ACT had a significantly increased risk of recurrence compared with ctDNA-negative patients. Conclusions: ctDNA is an independent prognostic factor, and this meta-analysis is a significant step for using ctDNA instead of historical prognostic factors in the adjuvant setting.

scholarly journals Magnetic and magnetodielectric coupling anomalies in the Haldane spin-chain system Nd2BaNiO5

AIP Advances ◽  
2015 ◽  
Vol 5 (3) ◽  
pp. 037128 ◽  
Author(s):  
Tathamay Basu ◽  
Niharika Mohapatra ◽  
Kiran Singh ◽  
E. V. Sampathkumaran
Keyword(s):  
Spin Chain ◽  
Chain System
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