Triangle Seminars
Tuesday, 26 Jan 2016
Eigenstate Phase Transitions for Strong Zero Modes
Paul Fendley
(Oxford)
Abstract:
Traditionally, most studies of quantum many-body systems have been mainly concerned with properties of the states of low-lying energy. Recently, however, fascinating features of the full energy spectrum have been uncovered. Among these are eigenstate phase transitions, where sharp transitions occur not only in the ground state, but in all the states. I describe a simple example of such, a transition for a strong zero mode in the XYZ spin chain. The strong zero mode is an operator that pairs states in different symmetry sectors, resulting in identical spectra up to exponentially small finite-size corrections. Such pairing occurs in the Ising/Majorana fermion chain and possibly in parafermionic systems and strongly disordered many-body localized phases. My proof here shows that the strong zero mode occurs in a clean interacting system, and that it possesses some remarkable structure – despite being a rather elaborate operator, it squares to the identity.
Traditionally, most studies of quantum many-body systems have been mainly concerned with properties of the states of low-lying energy. Recently, however, fascinating features of the full energy spectrum have been uncovered. Among these are eigenstate phase transitions, where sharp transitions occur not only in the ground state, but in all the states. I describe a simple example of such, a transition for a strong zero mode in the XYZ spin chain. The strong zero mode is an operator that pairs states in different symmetry sectors, resulting in identical spectra up to exponentially small finite-size corrections. Such pairing occurs in the Ising/Majorana fermion chain and possibly in parafermionic systems and strongly disordered many-body localized phases. My proof here shows that the strong zero mode occurs in a clean interacting system, and that it possesses some remarkable structure – despite being a rather elaborate operator, it squares to the identity.
Posted by: KCL
Thursday, 28 Jan 2016
One loop partition function of six dimensional conformal gravity using heat kernel on AdS_2n
Iva Lovrekovic
(Vienna)
Abstract:
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost, partially massless mode and massive mode.
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost, partially massless mode and massive mode.
Posted by: IC
Perturbative and numerical aspects of string sigma models
Lorenzo Bianchi
(DESY Hamburg)
Abstract:
In the last fifteen years an extensive and successful program has been carried out, consisting in the application of integrability techniques to the study of the AdS/CFT correspondence in the planar limit. In this talk we focus on a particular string background corresponding, on the dual side, to the expectation value of a cusped Wilson line. Recently the study of this background has been boosted by the OPE program for polygonal Wilson loops and scattering amplitudes. In this talk we consider the quantum fluctuations of the worldsheet theory around the null cusp classical solution and we investigate various quantities of physical interest (free energy, dispersion relation, S-matrix) in the perturbative expansion at strong coupling. We also propose a possible discretization of this model which can be used to study the theory non-perturbatively through numerical lattice simulations.
In the last fifteen years an extensive and successful program has been carried out, consisting in the application of integrability techniques to the study of the AdS/CFT correspondence in the planar limit. In this talk we focus on a particular string background corresponding, on the dual side, to the expectation value of a cusped Wilson line. Recently the study of this background has been boosted by the OPE program for polygonal Wilson loops and scattering amplitudes. In this talk we consider the quantum fluctuations of the worldsheet theory around the null cusp classical solution and we investigate various quantities of physical interest (free energy, dispersion relation, S-matrix) in the perturbative expansion at strong coupling. We also propose a possible discretization of this model which can be used to study the theory non-perturbatively through numerical lattice simulations.
Posted by: QMW