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Condensed Matter and Critical Phenomena
chaired by Alessandro Giuliani (Univ. Roma 3), Vieri Mastropietro (Univ. Milano), Alessandro Pizzo (Universita' di Roma "Tor Vergata")
from
to
(Europe/Rome)
at INFN  Laboratori Nazionali di Frascati ( Auditorium B. Touschek )
at INFN  Laboratori Nazionali di Frascati ( Auditorium B. Touschek )
Via Enrico Fermi, 40 00044 Frascati (RM)
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Support  cmcp2016@lists.lnf.infn.it 
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09:30
 10:30
Stability of FrustrationFree Ground States of Quantum Spin Systems
1h0'
Abstract: We study frustrationfree quantum lattice systems with a nonvanishing spectral gap above one or more (infinitevolume) ground states. The ground states are called stable if arbitrary perturbations of the Hamiltonian that are uniformly small throughout the lattice have only a perturbative effect. In the past several years such stability results have been obtained in increasing generality. We review results by BravyiHastings, BravyiHastingsMichalakis, and MichalakisZwolak, as well as recent refinements. (Joint work with Robert Sims and Amanda Young.)
Speaker: Prof. Bruno Nachtergaele (University of California, Davis) Material: Slides  10:30  11:00 Coffee Break

11:00
 12:00
Localization of interacting fermions with quasirandom disorder
1h0'
We consider interacting electrons in a one dimensional lattice with an incommensurate AubryAndre' potential in the regime when the singleparticle eigenstates are localized. We rigorously establish persistence of ground state localization in presence of weak manybody interaction, for almost all the chemical potentials. The proof uses a quantum many body extension of methods adopted for the stability of tori of nearly integrable hamiltonian systems, and relies on numbertheoretic properties of the potential incommensurate frequency.
Speaker: Prof. Vieri Mastropietro (Universita' di Milano) Material: Slides 
12:15
 13:15
Convergence of correlations in the 2D Ising model: primary fields and the stressenergy tensor
1h0'
In this talk we plan to summarize recent results on convergence of correlations functions in the critical 2D nearestneighbor Ising model (on general planar domains) to their continuous counterparts. This includes mixed correlations of spins, disorders, fermions and energy densities (in preparation, joint with Clement Hongler (Lausanne) and Konstantin Izyurov (Helsinki)) and a discrete version of the stressenergy tensor (arXiv:1604.06339, joint with Alexander Glaznam (TelAviv) and Stanislav Smirnov (Geneva)). The main technical tool is convergence theorems for discrete holomorphic spinors that are known to solve particular Riemanntype boundary value problems. In particular, one can construct all the aforementioned correlation functions and to deduce relevant CFT fusion rules starting with solutions to these Riemanntype boundary value problems in continuum.
Speaker: Prof. Dmitry Chelkak (ENS, Paris) Material: Slides  13:30  15:00 Lunch

15:00
 16:00
Precise critical exponents from Conformal bootstrap
1h0'
Originally formulated in the 70's, the conformal bootstrap is the ambitious idea that one can use internal consistency conditions to carve out, and eventually solve, the space of conformal field theories. In this talk I will review recent developments in the field which have boosted this program to a new level. I will present a method to extract quantitative informations in stronglyinteracting theories, such as 3D Ising, O(N) vector model and even systems without a Lagrangian formulation. I will explain how these techniques have led to the world record determination of several critical exponents.
Speaker: Prof. Alessandro Vichi ((Cern, Geneva))  16:00  17:00 Coffee Break & Discussion

09:30
 10:30
Stability of FrustrationFree Ground States of Quantum Spin Systems
1h0'


09:30
 10:30
Response in the topological insulators
1h0'
I shall discuss topological invariants of insulators and their response interpretation.
Speaker: Prof. Krzysztof Gawedzki (ENS de Lyon) Material: Slides  10:30  11:00 Coffee Break

11:00
 12:00
Universality and Hall transitions in interacting fermionic systems Abstract: In this talk I will discuss the charge transport properties of weakly interacting fermionic
1h0'
In this talk I will discuss the charge transport properties of weakly interacting fermionic systems, in the zero temperature and infinite volume limit. In the first part of the talk I will consider general interacting, gapped fermionic systems on periodic twodimensional lattices. Our theorem states that the Kubo conductivity matrix is independent of manybody interactions, provided the interaction strength is small enough. In particular, the result proves the stability of the integer quantum Hall effect against weak manybody interactions. In the second part of the talk, I will focus on the transitions between different topological Hall phases in the interacting Haldane model. The Haldane model is a graphenelike model that, in the absence of interactions, displays a nontrivial topological phase diagram. We consider the model in the presence of weak manybody interactions, and we give a rigorous construction of the renormalized transition line. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity do not depend on the interaction. The proofs are based on a combination of cluster expansion techniques, rigorous renormalization group and Ward identities. Joint work with A. Giuliani, I. Jauslin and V. Mastropietro.
Speaker: Prof. Marcello Porta Material: Slides 
12:15
 13:15
Invariant measures for nonlinear Schroedinger equations as limit of many body quantum states.
1h0'
We prove that Gibbs measures of nonlinear Schroedinger equations of Hartreetype arise as hightemperature limit of appropriately modified thermal states in manybody quantum mechanics. In dimensions d=2,3 these Gibbs measures are supported on singular distributions and Wick ordering of the interaction is necessary. Our proof is based on a perturbative expansion in the interaction, organised in a diagrammatic representation, and on Borel resummation of the resulting series. This is a joint work with J. Froehlich, A. Knowles and V. Sohinger.
Speaker: Prof. Benjamin Schlein (Univ. Zurich) Material: Slides  13:30  15:00 Lunch

15:00
 16:00
Bose Particles in a Box: Convergent Expansion of the Ground State
1h0'
I shall report on some recent works where I have introduced a multiscale analysis in the occupation numbers of particle states that provides a convergent expansion of the ground state of an interacting Bose gas in a finite box and in the mean field limiting regime. The talk will be mainly focussed on the construction of the ground state of a threemodes system.
Speaker: Prof. Alessandro Pizzo (Universita' di Roma "Tor Vergata") Material: Slides  16:00  17:00 Coffee Break & Discussion

09:30
 10:30
Response in the topological insulators
1h0'


09:30
 10:30
Kondo's effect in a hierarchical sd model and its perspectives.
1h0'
The hierarchical model for the sd model is simpler than the corresponding version of the Andrei kodel. But there is a precise relation between the RG flows for the two models which will be illustrated. Some properties of the beta function for the translation invariant (non hierarchical) Andrei's model will be also discussed.
Speaker: Prof. Giovanni Gallavotti (ROMA1) Material: Slides  10:30  11:00 Coffee Break

11:00
 12:00
Spectral properties of random regular graphs
1h0'
In this talk we plan to summarize recent results on convergence of correlations functions in the critical 2D nearestneighbor Ising model (on general planar domains) to their continuous counterparts. This includes mixed correlations of spins, disorders, fermions and energy densities (in preparation, joint with Clement Hongler (Lausanne) and Konstantin Izyurov (Helsinki)) and a discrete version of the stressenergy tensor (arXiv:1604.06339, joint with Alexander Glaznam (TelAviv) and Stanislav Smirnov (Geneva)). The main technical tool is convergence theorems for discrete holomorphic spinors that are known to solve particular Riemanntype boundary value problems. In particular, one can construct all the aforementioned correlation functions and to deduce relevant CFT fusion rules starting with solutions to these Riemanntype boundary value problems in continuum.
Speaker: Prof. Roland Bauerschmidt (University of Cambridge) 
12:15
 13:15
Order  Disorder operators in planar and almost planar graphs
1h0'
Speaker: Prof. Michael Aizenman (Princeton University) Material: Slides  13:30  15:00 Lunch

15:00
 16:00
Pfaffian Correlation Functions of Planar Dimer Covers
1h0'
In this talk I will explain an elementary derivation of the Pfaffian nature of boundary monomer correlation functions in the dimercovering problem on planar graphs. The boundary monomer correlation functions are then extended into a larger family of orderdisorder correlation functions which are shown to exhibit Pfaffian structure throughout the bulk. Key tools which will be discussed involve combinatorial switching symmetries which are identified through the loopgas representation of the double dimer model, and topological implications of planarity. This is joint work with Michael Aizenman and Manuel Lainz Valcazar.
Speaker: Prof. Simone Warzel (TU Munich) Material: Slides  16:00  17:00 Coffee Break & Discussion

09:30
 10:30
Kondo's effect in a hierarchical sd model and its perspectives.
1h0'