Logarithms in a non-unitary spin chain

For more info about our services contact : help@bestpfe.com

Table of contents

1 Introduction 
2 Bethe ansatz and related aspects 
2.1 Bethe ansatz
2.1.1 Notations and denitions
2.1.2 The ansatz
2.1.3 A word on numerically solving the Bethe equations
2.1.4 Admissible and non-admissible solutions
2.2 An additional TQ relation
2.2.1 Polynomiality of the other solution to the TQ relation
2.2.2 Polynomiality of P() and constructability of the Bethe state
2.2.3 An additional TQ relation
2.3 Geometrical models
2.3.1 Loop models
2.3.2 The Potts model
2.4 Identifying the continuum limit
2.4.1 Conformal eld theory
2.4.2 From the cylinder to the plane
2.4.3 Perturbation by irrelevant operators
2.4.4 A basic application of conformal invariance
3 Logarithms in a non-unitary spin chain 
3.1 Introduction
3.1.1 Overview
3.1.2 Denitions
3.2 OSp(1j2)
3.2.1 The spectrum from eld theory
3.2.2 The spectrum from the spin chain
3.2.3 Relation with 3-point functions
3.3 OSp(2j2)
3.3.1 The spectrum from eld theory
3.3.2 The spectrum from the spin chain
3.4 OSp(3j2)
3.4.1 The spectrum from the spin chain
3.5 Physical properties of fully packed trails
3.5.1 A model for loops with crossings
3.5.2 Inclusion of osp spectra
3.5.3 Charges and loop congurations
3.5.4 Transfer matrix eigenvalues and loop congurations
3.5.5 Watermelon 2-point functions for loops with crossings
3.5.6 Away from integrability
4 Excitation spectrum computation 
4.1 Introduction
4.1.1 Historical review
4.1.2 Euler-MacLaurin formula
4.1.3 An introductory example: the free fermions
4.2 A glance at the interacting case: revisiting the free fermions
4.3 Finite-size corrections in the interacting case
4.3.1 Presentation
4.3.2 Properties of the distribution S
4.3.3 Computing the shift I
4.3.4 The momentum
4.3.5 The energy
4.4 Strings
4.4.1 Denitions and notations
4.4.2 Riemann sums with logarithmic singularities
4.4.3 Computing the shifts Iq
4.4.4 The energy
4.5 Logarithmic corrections
4.5.1 Presentation
4.5.2 Computing B1
4.5.3 Logarithmic corrections to the energy
4.5.4 Examples and numerical checks
5 Series expansions and magnetic eld inuence 
5.1 Introduction
5.2 The XXZ spin chain in a magnetic eld
5.2.1 Historical review
5.2.2 The Bethe equations as a recurrence relation
5.2.3 Example: the Heisenberg spin chain
5.2.4 Example: the XXZ spin chain
5.2.5 Radius of convergence of the series ( p hc 􀀀 h)
5.2.6 An example with complex roots
5.2.7 Finite-size corrections and critical exponents
5.3 Some intermediate results on a non-compact spin chain
5.3.1 Motivations
5.3.2 A dual recurrence relation
5.3.3 Analytic continuation at m = 􀀀1
5.3.4 Perspectives
5.4 Fluctuations inside the arctic curve in the interacting six-vertex model
5.4.1 Presentation
5.4.2 The free energy F(x; y)
5.4.3 The free fermion case = 0
5.4.4 Value of K(mx;my) in the interacting case
5.4.5 Numerical checks
A 
A.1 Change of grading
A.2 Proof of Lemma 4
A.3 Proof of Lemma 6
A.4 Proof of Lemma 7
A.5 Proof of Lemma 8