Quantum Encounters Seminar

The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and high-energy systems. In this work, we perform an exact microscopic study of such a complex CFT (CCFT) in the two-dimensional O(n) loop model. The well-known absence of symmetry-breaking of the O(n>2) model is understood as arising from the displacement of the non-trivial fixed points into the complex temperature plane. Thanks to a numerical finite-size study of the transfer matrix, we confirm the presence of a CCFT in the complex plane and extract the real and imaginary parts of the central charge and scaling dimensions. By comparing those with the analytic continuation of predictions from Coulomb gas techniques, we determine the range of validity of the analytic continuation to extend up to n_g≈12.34, beyond which the CCFT gives way to a gapped state. Finally, we propose a beta function which reproduces the main features of the phase diagram and which suggests an interpretation of the CCFT as a liquid-gas critical point at the end of a first-order transition line. 

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Landau's theory of Fermi liquids is a cornerstone of theoretical physics. I will show how to formulate Fermi liquid theory as an effective field theory of bosonic degrees of freedom, using the mathematical formalism of coadjoint orbits. While at the linear level, this theory reduces to existing multidimensional bosonization approaches, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response, such as higher-point functions of currents. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior, and provides a computationally advantageous approach for non-Fermi liquids -- strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions.

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In this talk I will describe constraints from causality and unitarity on 2→2 graviton scattering in weakly-coupled gravitational effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, I will explain how to derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Such bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis. In addition they demonstrate the gravity must be weakly coupled at all scales below Planck. Time permitting, I will comment on the experimental implications of the bounds.

Sujet : Quantum Encounter Seminar
Heure : 17 mai 2022 04:00 PM Paris

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Lattice gauge theories, when restricted to the pure gauge sector (i.e. no matter, only gauge fields), typically show a phase transition between a topologically-ordered deconfined phase at weak coupling and a trivial confined phase at strong coupling (cf. Wegner 1971, Wilson 1974, Fradkin and Shenker 1979). The diagnosis for such a topological phase transition is a non-local gauge-invariant order parameter known as a Wegner-Wilson loop (WWL) defined along a chosen contour. The WWL features a perimeter law exp(-#P) in the topological phase and an area law exp(-#A) in the confined phase, where P is the perimeter and A the area of the contour. The trivial phase is described as having confined charges (“quark confinement”) and condensed fluxes. Whereas, the topological phase has free (deconfined) charges and fluxes. Two-dimensional quantum lattice gauge theories are special in that the excitations in the deconfined phase are anyons (cf. toric code model, Kitaev 2003). In the toric code, WWL were studied in detail by Halasz and Hamma 2012.

Here we extend such a study of WWL from lattice gauge theories built on gauge groups to string-net models (Levin-Wen 2005) built on more general objects known as unitary modular tensor categories. We use these WWL to study the different kind of anyonic excitations that are believed to be described at low-energy by a topological quantum field theory of the doubled achiral type.

Ref: A. Ritz-Zwilling, J.-N. Fuchs and J. Vidal, arxiv:2011.12609,  Phys. Rev. B 103, 075128 (2021).

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- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
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without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe quantum_encounters_seminar PRENOM NOM"
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The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this paper we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, that connects to the known d = 26, 10 when the deformation is removed. En passant, we find that the Veneziano amplitudes can be extended to massive scalars of masses up to m^2 = 1/3, where it has critical dimension 6.3. On the low-energy side, we compute the first few couplings of the theory in terms of q-deformed analogues of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance.

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IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe quantum_encounters_seminar PRENOM NOM"
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I will talk about a new type of critical quantum liquids, dubbed Stiefel liquids, that can emerge in quantum magnets. Our theory is based on 2+1 dimensional nonlinear sigma models on target space SO(N)/SO(4), supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of 3d CFTs with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid (i.e. Nf=4 QED3) are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, we conjecture that Stiefel liquids with N>6 are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. I will also discuss a physical way to realize Stiefel liquids (both the Dirac spin liquid and N=7 non-Lagrangian Stiefel liquid) in quantum spin systems, for example, on triangular or kagome lattice, through the intertwinement of symmetry breaking orders.

Participer à la réunion Zoom
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IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 70 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 70 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe quantum_encounters_seminar PRENOM NOM"
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Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree.

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I will explain how the conformal bootstrap can be adapted to place rigorous bounds on the spectra of automorphic forms on locally symmetric spaces. A locally symmetric space is of the form H\G/K, where G is a non-compact semisimple Lie group, K the maximal compact subgroup of G, and H a discrete subgroup of G. If we take G = SL(2,R), then spaces of this form are precisely hyperbolic surfaces and hyperbolic 2-orbifolds. Automorphic forms then come in two types: modular forms, and eigenfunctions of the hyperbolic Laplacian, also known as Maass forms. The bootstrap constraints arise from the associativity of function multiplication on the space H\G, and are very similar to the usual correlator bootstrap equations, with G playing the role of the conformal group. For G=SL(2,R), I will use this method to prove upper bounds on the lowest positive eigenvalue of the Laplacian on all closed hyperbolic surfaces of a fixed genus. The bounds at genus 2 and genus 3 are very nearly saturated by the Bolza surface and the Klein quartic. This is based on upcoming work with P. Kravchuk and S. Pal.

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We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types  of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear luttinger liquid, their structure is more complicated and not understood.

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In the Heisenberg picture of quantum mechanics, time evolution is a one-parameter family of automorphisms of operator algebra. Restricted to short times the equivalence between time evolution and quantum circuits, especially the property that it maps a local operator to another, has been implanted in theoretical studies of topological phases of matter. In this talk, I will explain recent findings that not all locality-preserving automorphisms, also called quantum cellular automata, can be written as quantum circuits --- there exists a "discrete time dynamics" that cannot have a "Hamiltonian." These are tightly related to static, topological many-body states. I will give results on the classification of these automorphisms, and connect them to locally generated subalgebras in one lower dimension.

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The Berry phase is a well-known phenomenon in quantum mechanics with many profound implications. It describes the response of the phase of the wavefunction to the adiabatic evolution of system parameters, defining a U(1) connection on the parameter space. In many-body systems described by quantum field theory, we may also allow the parameters to vary in space, and we find a higher group connection generalizing the Berry phase. This connection also describes phenomena such as the Thouless pump and its generalizations. It allows us to constrain the global structure of phase diagrams by probing non-contractible cycles in the space of quantum field theories. In a typical phase diagram drawn in R^n, these cycles surround topologically-protected critical loci called diabolical points, in analogy to the quantum mechanical singularities which act as "monopoles" for the Berry connection. I will discuss these concepts in more detail, as well as a bulk-boundary correspondence and some recent applications to phase diagrams of topologically ordered systems. This talk is based on https://arxiv.org/abs/2004.10758 w/ Po-Shen Hsin and Anton Kapustin https://arxiv.org/abs/2110.07599 and its sequel, 2110.xxxx w/ Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen.

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A many-body quantum system that is continually monitored by an external observer can be in two distinct dynamical phases, distinguished by whether or not repeated local measurements (throughout the bulk of the system) prevent the build-up of long-range quantum entanglement. I will describe the key features of such “measurement phase transitions” and sketch theoretical approaches to their critical properties that make connections with topics in classical statistical mechanics, such as percolation and disordered magnetism. Finally I will discuss random tensor networks with a tree geometry. These arise in a simple limit of the measurement problem, and they show an entanglement transition that can be solved exactly by a mapping to a problem of traveling waves.

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IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe quantum_encounters_seminar PRENOM NOM"
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Emergence is a major buzz word of our times. My working definition, which gives plenty of room for manoeuvre is: the appearance of many body phenomena of higher symmetry than that of the Hamiltonian and degrees of freedom at the microscopic level.

In this colloquium I will discuss a topical example - the frustrated magnetic material, spin ice. Here, to an excellent approximation a classical field theoretic description with continuous U(1) symmetry emerges from Ising like degrees of freedom. The associated quasi-particles appear to be freely moving magnetic charge - magnetic monopoles - and the system behaves as a magnetic Coulomb fluid in the grand canonical ensemble with intrinsic topological properties. With the addition of quantum fluctuations the emergent magneto-statics develops further into a complete analogue of quantum electrodynamics. I will aliment this discussion with experimental results from a wide range of systems.

https://us02web.zoom.us/j/85270888147?pwd=aXdOVXBTSmNEU00vVFE2bXhqdE5vdz09

ID de réunion : 852 7088 8147
Code secret : 276852

Recently methods of quantum statistical mechanics have been fruitfully applied to the study of phases of quantum lattice systems at zero temperature. For example, a rigorous definition of a Short-Range Entangled phase of matter has been given and a classification of such phases in one spatial dimension has been achieved. I will discuss some of these developments, focusing on the topology and geometry of the space of Short-Range Entangled states. According to a conjecture of A. Kitaev, these spaces form a loop spectrum in the sense of homotopy theory. This conjecture implies that to any family of Short-Range entangled states in one dimension one can associate a gerbe on the parameter space. I will show how to construct such a gerbe. Thе curvature of this gerbe is a closed 3-form with quantized periods and can be regarded as a higher-dimensional generalization of the curvature of the Berry connection.

https://us02web.zoom.us/j/81778962715?pwd=QnpNS2ErSnBCTWRYUHphd1VMMysyZz09

ID de réunion : 817 7896 2715
Code secret : 800452