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 )
Via Enrico Fermi, 40 00044 Frascati (RM)
Description
The workshop aims at presenting recent results in the mathematical theory of critical phenomena and effective theories in condensed matter physics and statistical mechanics, including: scaling limits of discrete spin systems, percolation models and interacting random walks; effective dynamics and phase transitions in interacting quantum many body systems; disordered electrons and localization phenomena.

Invited speakers include
M. Aizenman, R. Bauerschmidt, D. Chelkak, G. Gallavotti, K. Gawedzki, V. Mastropietro, B. Nachtergaele, A. Pizzo,  M. Porta, B. Schlein,  A. Vichi, S. Warzel

Organizers:
A. Giuliani, V. Mastropietro, A. Pizzo
 
 
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Go to day
  • Monday, 5 September 2016
    • 09:30 - 10:30 Stability of Frustration-Free Ground States of Quantum Spin Systems 1h0'
      Abstract: We study frustration-free quantum lattice systems with a non-vanishing spectral gap above one or more
      (infinite-volume) 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
      Bravyi-Hastings, Bravyi-Hastings-Michalakis, and Michalakis-Zwolak, as well as recent refinements. (Joint
      work with Robert Sims and Amanda Young.)
      Speaker: Prof. Bruno Nachtergaele (University of California, Davis)
      Material: Slides pdf file}
    • 10:30 - 11:00 Coffee Break
    • 11:00 - 12:00 Localization of interacting fermions with quasi-random disorder 1h0'
      We consider interacting electrons in a one dimensional lattice with an incommensurate Aubry-Andre' potential in the regime when the single-particle eigenstates are localized. We rigorously establish persistence of ground state localization in presence of weak many-body 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 number-theoretic properties of the potential incommensurate frequency.
      Speaker: Prof. Vieri Mastropietro (Universita' di Milano)
      Material: Slides pdf file}
    • 12:15 - 13:15 Convergence of correlations in the 2D Ising model: primary fields and the stress-energy tensor 1h0'
      In this talk we plan to summarize recent results on convergence of correlations functions in
      the critical 2D nearest-neighbor 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 stress-energy tensor (arXiv:1604.06339, joint with Alexander Glaznam (Tel-Aviv) and Stanislav Smirnov (Geneva)). The main technical tool is convergence theorems for discrete holomorphic spinors that are known to solve particular Riemann-type 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 Riemann-type boundary value problems in continuum.
      Speaker: Prof. Dmitry Chelkak (ENS, Paris)
      Material: Slides pdf file}
    • 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 strongly-interacting 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
  • Tuesday, 6 September 2016
    • 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 pdf file}
    • 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 two-dimensional lattices.  Our theorem states that
      the Kubo conductivity matrix is independent of many-body interactions, provided the interaction strength is
      small enough. In particular, the result proves the stability of the integer quantum Hall effect against weak
      many-body 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 graphene-like model that, in
      the absence of interactions, displays a non-trivial topological phase diagram. We consider the model in the
      presence of weak many-body 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 pdf file}
    • 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 Hartree-type arise as
      high-temperature limit of 
      appropriately modified thermal states in many-body 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 pdf file}
    • 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 
      multi-scale 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
      three-modes system.
      Speaker: Prof. Alessandro Pizzo (Universita' di Roma "Tor Vergata")
      Material: Slides pdf file}
    • 16:00 - 17:00 Coffee Break & Discussion
  • Wednesday, 7 September 2016
    • 09:30 - 10:30 Kondo's effect in a hierarchical s-d model and its perspectives. 1h0'
      The hierarchical model for the s-d 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 pdf file}
    • 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 nearest-neighbor 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 stress-energy tensor (arXiv:1604.06339, joint with Alexander Glaznam (Tel-Aviv) and Stanislav Smirnov (Geneva)). The main technical tool is convergence theorems for discrete holomorphic spinors that are known to solve particular Riemann-type 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 Riemann-type 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 pdf file}
    • 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 dimer-covering problem on  planar graphs.  
      The boundary monomer correlation functions are then extended into a larger family of order-disorder 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 loop-gas 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 pdf file}
    • 16:00 - 17:00 Coffee Break & Discussion