scholarly journals Branch point twist field form factors in the sine-Gordon model I: Breather fusion and entanglement dynamics

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Olalla Castro-Alvaredo ◽  
David Horvath
Keyword(s):  
Branch Point ◽  
Form Factors ◽  
Building Blocks ◽  
Small Mass ◽  
Particle Spectrum ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Fusion Procedure ◽  
Particle Form ◽  
Sine Gordon Model

The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap program. In this paper we compute low particle-number form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory possesses a particle spectrum consisting of a soliton, an antisoliton (of opposite U(1) charges) and several (neutral) breathers. In the breather sector we exploit the fusion procedure to compute form factors of heavier breathers from those of lighter ones. We apply our results to the study of the entanglement dynamics after a small mass quench and for short times. We show that in the presence of two or more breathers the von Neumann and Rényi entropies display undamped oscillations in time, whose frequencies are proportional to the even breather masses and whose amplitudes are proportional to the breather's one-particle form factor.

scholarly journals An Operator Product Expansion for Form Factors II. Born level

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Amit Sever ◽  
Alexander G. Tumanov ◽  
Matthias Wilhelm
Keyword(s):  
Form Factor ◽  
Operator Product Expansion ◽  
Wilson Loop ◽  
Form Factors ◽  
Building Blocks ◽  
Operator Product ◽  
Yang Mills ◽  
Singlet States ◽  
Particle Form ◽  
Elementary Building

Abstract Form factors in planar $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in [1]. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.

scholarly journals Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

2019 ◽  
Vol 20 (12) ◽  
pp. 3889-3926
Author(s):  
Henning Bostelmann ◽  
Daniela Cadamuro
Keyword(s):  
Bound States ◽  
Von Neumann Algebras ◽  
Form Factors ◽  
Explicit Construction ◽  
Local Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Von Neumann ◽  
Local Observables ◽  
Wightman Axioms

Abstract We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh–Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model.

scholarly journals ENTANGLEMENT DYNAMICS IN FINITE QUDIT CHAIN IN CONSISTENT MAGNETIC FIELD

2012 ◽  
Vol 10 (06) ◽  
pp. 1250068 ◽  
Author(s):  
E. A. IVANCHENKO
Keyword(s):  
Magnetic Field ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Magnetic Field Modulation ◽  
Entanglement Measures ◽  
Analytical Formulae ◽  
Initial States ◽  
Von Neumann Equation ◽  
Field Modulation ◽  
The Magnetic Field

Based on the Liouville–von Neumann equation, we obtain a closed system of equations for the description of a qutrit or coupled qutrits in an arbitrary, time-dependent, external magnetic field. The dependence of the dynamics on the initial states and the magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in bi-qudits with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulae for the entanglement measures in finite chains from two to six qutrits or three quartits are presented.

Piezoelectric Thin Film AlN Annular Dual Contour Mode Bandpass Filter

2005 ◽  
Author(s):  
Philip J. Stephanou ◽  
Gianluca Piazza ◽  
Carolyn D. White ◽  
Muthu B. J. Wijesundara ◽  
Albert P. Pisano
Keyword(s):  
Bandpass Filter ◽  
Form Factors ◽  
Building Blocks ◽  
Experimental Characterization ◽  
Modes Of Vibration ◽  
Fabrication Tolerances ◽  
Piezoelectric Thin Film ◽  
Device Sensitivity ◽  
Contour Mode

The following work presents the analytical, numerical and experimental characterization of a novel piezoelectric Aluminum Nitride MEMS bandpass filter. In contrast to multipole filters employing distinct mechanically or electrically coupled resonator building blocks, the passband of the device in the present work is defined by the proximity of two natural contour modes of vibration in a single annular resonator. The proposed implementation, albeit currently limited to dual-pole filters, results in smaller form factors and reduces device sensitivity to across wafer fabrication tolerances.

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