UK Meeting on Integrable and Conformal Field Theory

The meeting will be held at the Strand Campus of King's College London.

All the talks be in room S-3.20 of the Strand Campus (take the lifts down to floor -3 from the main entrance on the Strand).

Registration and coffee on Friday will be in S-2.23 of the Strand Campus (take the lifts down to floor -2 from the main entrance on the Strand).

The meeting is scheduled to begin after lunch on Friday 10th June, and continue until lunchtime on Saturday 11th June.

**Provisional Timetable**

Friday, June 10 | |||

14.00-14.45 | Registration - coffee & tea - room S-2.23 | ||

14.45-15.30 | Daniele Dorigoni | ||

Resurgence in eta-deformed Principal Chiral Models (abstract) | |||

15.30-16.00 | Jennifer Ashcroft | ||

Scattering Sheep: Kink Collisions in the Presence of False Vacua (abstract) | |||

16.00-16.30 | Thomas Dupic | ||

Lattice models with a W (abstract)_{3} conformal limit | |||

16.30-17.00 | Break - room S-2.23 | ||

17.00-17.45 | Ingo Runkel | ||

Perturbed defects and integrability in 2d CFT (abstract) | |||

17.45-18.15 | Isao Makebe | ||

(Super) conformal defects in the tricritical Ising model (abstract) | |||

Dinner | 19.00, Thai Square Strand | ||

Saturday, June 11 | |||

10.00-10.45 | Robert Konik | ||

Studies of the Loschmidt Echo in Two Dimensional Coupled Arrays of
Quantum Ising Chains and Luttinger Liquids: (abstract)Combining Truncated Hamiltonian Methods with Matrix Product States | |||

10.45-11.15 | Márton Kormos | ||

Truncated Hamiltonian approach to quantum quenches in the Ising field theory (abstract) | |||

11.15-11.45 | Break | ||

11.45-12.30 | Olalla Castro-Alvaredo | ||

Universal Quantum Field Theory Quantities from Measures of Entanglement: (abstract)The Logarithmic Negativity | |||

12.30-13.00 | Tamas Palmai | ||

Entanglement Entropy from the Truncated Conformal Space (abstract) |

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IoP members should note there is a Carers fund that can help meet extra expenses needed to attend worshops and conferences and the LMS has a similar fund open to all UK mathematicians.

**Abstracts**

Daniele Dorigoni | |

Resurgence in eta-deformed Principal Chiral Models | |

Abstract TBA | |

Jennifer Ashcroft | |

Scattering Sheep: Kink Collisions in the Presence of False Vacua | |

We investigate numerically head-on kink collisions in a 1+1 dimensional scalar field theory with multiple vacua. The lowest minimum of the potential is called the true vacuum, and any local minima with higher energy are called false vacua. We consider kinks interpolating between false and true vacua, and form four distinct initial configurations from combinations of these kinks. A rich variety of scattering outcomes is found in which, depending on the initial kink set-up and impact velocities, kinks can repel each other, annihilate, form true or false domain walls and reflect off each other. | |

Thomas Dupic | |

Lattice models with a W_{3} conformal limit | |

Loop models are lattice models usually describing extended geometrical objects such as interfaces. In the continuum limit they are described by non-rational conformal field theories (CFTs) with a discrete spectrum. The most well-known of those models is O(n), whose scaling limit gives a realisation of the Virasoro algebra.
Another interesting loop model is the fully packed loop (FPL) model. On the cylinder (or the annulus) this model is known to be exactly equivalent to the SU(3) RSOS model, provided non contractible loops have the correct weight. This suggests that in the scaling limit the (twisted) FPL loop model renormalizes towards a CFT with an extended W_{3} symmetry. Our motivation is to study the link between this twisted FPL loop model and the known CFTs with extended W_{3} symmetry (minimal models) in more details. On the cylinder we use exact diagonalization to extract the finite size spectrum. We also compute analytically the torus partition function of the FPL model in the continuum, from which the full spectrum can be extracted. The extended symmetry is manifest in the counting of descendants. As was the case for the O(n) model, the spectrum contain states with fractional Kac indices (fractional electric charges). The RSOS and FPL loop models are no longer equivalent on the torus, and in particular they have different partition function in the continuum. | |

Ingo Runkel | |

Perturbed defects and integrability in 2d CFT | |

2d CFTs describe universality classes of critical behaviour of 2d statistical systems. If the statistical system is integrable, one would expect this to be reflected in its universality class. One is thus led to the question of understanding integrability from within a given 2d CFT. In this talk I will present one way to do this by studying line defects of the 2d CFT and their perturbations. The perturbed defects give rise to families of conserved charges and allow one to determine their functional relations. | |

Isao Makebe | |

(Super) conformal defects in the tricritical Ising model | |

Using the ideas of Gang and Yamaguchi (arXiv:0809.0175 [hep-th]) we study conformal defects in the N=1 super-Virasoro minimal model SM(3,5) obtained by folding SM(10,12) D6-E6 invariant theory. We show some of the factorising defects cannot be obtained from folding. | |

Robert Konik | |

Studies of the Loschmidt Echo in Two Dimensional Coupled Arrays of
Quantum Ising Chains and Luttinger Liquids:Combining Truncated Hamiltonian Methods with Matrix Product States | |

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions. The method combines the benefits of integrability and matrix product states in one dimension. In particular it can be extended to systems whose geometry is that of an infinitely long cylinder. As example applications we present results for quantum quenches in both arrays of coupled quantum Ising chains and coupled Luttinger liquids. In quenches that cross a phase boundary we find that the return probability shows non-analyticities in time. | |

Márton Kormos | |

Truncated Hamiltonian approach to quantum quenches in the Ising field theory | |

The recent experimental progress in cold atomic physics and quantum circuits poses challenging fundamental questions on quantum systems out of equilibrium and calls for the development of new theoretical methods. Compared to lattice systems, the dynamics of continuum systems is much more difficult to study. I will show that the truncated Hilbert space appoach can be an efficient method for studying the non-equilibrium time evolution of field theories regardless of their integrability by applying it to quenches in the 1D Ising field theory. After benchmarking the method with analytical results in the integrable case, I will report new results for non-integrable quenches that instead of a prethermalization scenario show persistent oscillations and in the ferromagnetic phase strong effects of confinement. | |

Olalla Castro-Alvaredo | |

Universal Quantum Field Theory Quantities from Measures of Entanglement:The Logarithmic Negativity | |

In this talk I will review some recent work where we have studied a measure of entanglement known as logarithmic negativity (LN) in the context of 1+1 dimensional massive Quantum Field Theory (QFT). I will present some very general results regarding the behaviour of the LN in massive QFT in particular limits. These results are based on expressing the LN in terms of a correlation function of branch point twist fields. I will explain how a more general study of the two-point functions of twist fields can give us access to universal QFT quantities such as expectation values and structure constants (at the conformal point) which are otherwise very hard to access. I will show some numerical (unpublished) results which illustrate this for the massive free Boson theory. | |

Tamas Palmai | |

Entanglement Entropy from the Truncated Conformal Space | |

A new numerical approach to entanglement entropies of the Renyi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited to study the crossover from massless to massive behavior when the subsystem size is comparable to the correlation length. The calculation relies on exact four point functions of descendant fields. We apply this method to ground and excited states in different deformations of massless free fermions, corresponding to the scaling limit of the Ising model in transverse and longitudinal fields. |

Further details will be available here in due course.