scholarly journals Symmetry resolved entanglement in integrable field theories via form factor bootstrap

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Dávid X. Horváth ◽  
Pasquale Calabrese
Keyword(s):  
Form Factor ◽  
Integrable Field Theories ◽  
Field Theories ◽  
Von Neumann Entropy ◽  
Matrix Elements ◽  
Von Neumann ◽  
Bootstrap Approach ◽  
Complete Computation ◽  
Twist Fields ◽  
Integrable Field

Abstract We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in an intuitive way and their solution is presented for the massive Ising field theory and for the genuinely interacting sinh-Gordon model, both possessing a ℤ2 symmetry. The solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. The issue of symmetry resolution for discrete symmetries is also discussed. We show that entanglement equipartition is generically expected and we identify the first subleading term (in the UV cutoff) breaking it. We also present the complete computation of the symmetry resolved von Neumann entropy for an interval in the ground state of the paramagnetic phase of the Ising model. In particular, we compute the universal functions entering in the charged and symmetry resolved entanglement.

scholarly journals U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dávid X. Horváth ◽  
Luca Capizzi ◽  
Pasquale Calabrese
Keyword(s):  
Form Factor ◽  
Branch Point ◽  
Complete Solution ◽  
Form Factors ◽  
Vacuum Expectation ◽  
Field Theories ◽  
The Novel ◽  
Bootstrap Approach ◽  
Twist Fields

Abstract We generalise the form factor bootstrap approach to integrable field theories with U(1) symmetry to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are solved for the free massive Dirac and complex boson theories, which are the simplest theories with U(1) symmetry. We present the exact and complete solution for the bootstrap, including vacuum expectation values and form factors involving any type and arbitrarily number of particles. The non-trivial solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. An alternative and compact determination of the novel form factors is also presented. Based on the form factors of the U(1) composite branch-point twist fields, we re-derive earlier results showing entanglement equipartition for an interval in the ground state of the two models.

SINGLE q-OSCILLATOR MODE REALIZATION OF QUANTUM GROUP THROUGH CANONICAL BOSONIZATIONS OF SU(2)q AND q-OSCILLATORS

1991 ◽  
Vol 06 (08) ◽  
pp. 701-705 ◽  
Author(s):  
B. BASU MALLICK ◽  
A. KUNDU
Keyword(s):  
Integrable Field Theories ◽  
Quantum Group ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Sine Gordon Model ◽  
Integrable Field

Canonical action-angle type bosonizations of SU(2)q and q-oscillators found by us lead to a novel single q-oscillator mode realization of quantum group, representing a q-deformed Holstein-Primakoff transformation. The same canonical bosonizations help us to find a deforming map for q-oscillators, which in turn induces deforming functionals for centreless Virasoro algebra. Such bosonizations are also shown to play an important role in generating integrable field theories like sine-Gordon model.

scholarly journals CLASSICALLY INTEGRABLE FIELD THEORIES WITH DEFECTS

2004 ◽  
Vol 19 (supp02) ◽  
pp. 82-91 ◽  
Author(s):  
P. BOWCOCK ◽  
E. CORRIGAN ◽  
C. ZAMBON
Keyword(s):  
Integrable Field Theories ◽  
Boundary Conditions ◽  
Scalar Fields ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Internal Boundary ◽  
Liouville Type ◽  
Real Scalar ◽  
Integrable Field

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.

scholarly journals INTEGRABLE FIELD THEORIES DERIVED FROM 4-D SELF-DUAL GRAVITY

1996 ◽  
Vol 11 (07) ◽  
pp. 545-552 ◽  
Author(s):  
TATSUYA UENO
Keyword(s):  
Integrable Field Theories ◽  
Sigma Models ◽  
Einstein Equation ◽  
Differential Form ◽  
The Self ◽  
Higgs Bundle ◽  
Field Theories ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Integrable Field

We reformulate the self-dual Einstein equation as a trio of differential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2-D sigma models valued in infinite-dimensional group, which was shown by Park and Husain earlier. We also derive other field theories including the 2-D Higgs bundle equation. This formulation elucidates the relation among these field theories.

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