TALKS

May 16 (Mon)


  • David Berenstein (UC Santa Barbara)
    Title: Aspects of the Quantum Mechanical Bootstrap
    Abstract: I will detail some recent advances in understanding how to solve one dimensional quantum mechanical problems with the numerical Bootstrap method for problems in the real line, the circle and the positive real axis. Numerically, convergence seems to be exponential in the real line and the positive real axis problem. For the circle problem, one obtains the band structure of the potential. Finally, I will describe some additional progress when dealing with Robin boundary conditions on the positive real axis problem.


  • Robert de Mello Koch (University of Witwatersrand)
    Title: Numerical Loop Space for Multi-matrix systems
    Abstract: We revisit the problem of solving multi-matrix quantum mechanics, at large N, numerically. The approach adopted uses collective field theory to give a loop space representation of the dynamics, leading to a constrained optimization problem. The constraint is solved using a master-field parametrization. The complete fluctuation spectrum is also computable in the above scheme, and is of immediate physical relevance. The numerical results presented prove that this approach solves, by numerical loop space methods, the general two matrix model problem.


  • Frank Pollmann (TUM)
    Title: Exploring Quantum Phases of Matter on Quantum Processors
    Abstract:     The interplay of quantum fluctuations and interactions can yield novel quantum phases of matter with fascinating properties. Particularly exciting physics is at play when confining systems to two spatial dimensions. For this case it has been predicted that exotic quantum particles emerge —so-called “anyons”— that cannot exist in the three-dimensional world we live in. Understanding the physics of such system is a very challenging problem as it requires to solve quantum many body problems—which is generically exponentially hard on classical computers.

In this context, universal quantum computers are potentially an ideal setting for simulating the emergent quantum many-body physics. In my talk, I will discuss how to use existing (noisy) quantum computers to simulate quantum phases of matter. First, I will consider symmetry protected topological phases (SPT) in one-dimensional systems. For this case, ground states of Hamiltonians can be obtained using shallow quantum circuits and we can observe a quantum phase transition between different SPT phases on a quantum device. Second, we prepare the ground state of the toric code Hamiltonian in two-dimensions using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of ln(2), and simulate anyon interferometry to extract the characteristic braiding statistics of the emergent excitations.


  • Masanori Hanada (University of Surrey)
    Title: Black Hole from Matrices
    Abstract: Matrix models can describe black hole via holography. I will review numerical approaches which were successful in the past, and discuss the necessity of new methods for tackling certain fascinating problems.

May 17 (Tue)


  • Pietro Brighi (IST Austria)
    Title:     Tensor network approaches to the study of the interplay of large localized systems and small thermal grains
    Abstract:     In isolated quantum many-body systems, thermalization is believed to occur due to the ergodicity of the system. While most physical systems indeed behave in an ergodic way and their dynamics leads to thermal equilibrium, some outstanding counterexamples exist. Many-body localization (MBL) provides a paradigmatic case of ergodicity-breaking, where strong disorder leads to the lack of relaxation to the thermal equilibrium.

In this talk I will present recent studies of the interplay of large non-interacting localized chains and small ergodic baths. Using matrix product state (MPS) methods, we probe the dynamics of these systems, showing that in the strong interaction case not only the localized chain does not thermalize, but it also leads to the localisation of the bath, a phenomenon known as MBL proximity effect. The presence of the thermal inclusion, however, leads to a dramatic change in the system, as it makes the localized particles interact. As a consequence, interesting entanglement patterns arise in the chain, a feature we dubbed propagation of MBL. Thanks to a phenomenological theory, we are able to link the localisation of the thermal grain and the phenomenon of propagation of MBL, reproducing the characteristic entanglement behavior.


  • Kazuki Yamamoto (Kyoto University)
    Title:     Finite-size scaling in a non-Hermitian XXZ spin chain
    Abstract:     In recent years, open quantum systems have been actively studied both experimentally and theoretically, as exemplified by driven-dissipative systems and non-Hermitian (NH) quantum systems. In this talk, We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in one-dimensional open quantum many-body systems [1]. Our analytic calculation is based on effective field theory with bosonization, finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. Our numerical analysis is based on the density-matrix renormalization group generalized to non-Hermitian systems (NH-DMRG). We uncover that the model in the massless regime with weak dissipation belongs to the universality class characterized by the complex-valued TL parameter, which is related to the complex generalization of the c=1 conformal field theory. As the dissipation strength increases, the values of the TL parameter obtained by the NH-DMRG begin to deviate from those obtained by the Bethe-ansatz analysis, indicating that the model becomes massive for strong dissipation. Our results can be tested with the two-component Bose-Hubbard system of ultracold atoms subject to two-body loss.

[1] Kazuki Yamamoto, Masaya Nakagawa, Masaki Tezuka, Masahito Ueda, and Norio Kawakami, arXiv:2112.12467, Phys. Rev. B in press.


  • Fabien Alet (CNRS)
    Title:     Interior eigenvalue problem for localisable quantum lattice models in condensed matter
    Abstract:     I will provide an overview of numerical techniques that have been proposed to obtain eigenstates deep in the middle of the spectrum of many-body quantum systems. This problem is particularly relevant for systems which do not follow the eigenstate thermalization hypothesis. I will discuss spectral transforms methods -- trying to review different strategies and works --, and focus in particular ont the shift-invert technique. Examples of applications in the field of many-body localization will also be presented. In conclusion, perspectives will be given on how to perhaps improve these methods and applications to other fields.


  • David Luitz (University of Bonn)
    Title:     Krylov space time evolution and quantum typicality
    Abstract:     I will discuss how to perform exact time evolution of many-body wave functions using Krylov space algorithms. This method only relies on a fast matrix vector product of the Hamiltonian (or the evolution operator) and is the only method which can deal with similarly large systems in the regime of strong entanglement, which is generically produced over time. In combination with the concept of quantum typically, which allows us to get rid of traces over operators, this method develops its full power. I will demonstrate this power with the example of how to calculate out of time order correlators in Heisenberg spin chains with short and long range interactions.

May 18 (Wed)


  • Raghav Jha (Perimeter Institute)
    Title:     New approach to continuous spin models in two and three dimensions
    Abstract:     We apply tensor network methods to study the famous phase transition in the two-dimensional O(2) model and a generalized version of this model that admits half-integer vortices in addition to the standard integer ones. We then consider the same model in three dimensions and carry out the first tensor study and locate the continuous phase transition. Furthermore, we introduce finite chemical potential and explore the Silver Blaze phenomenon by computing the particle number density. While the addition of chemical potential leads to a non-real action and is not suited for the standard Monte Carlo, it is straightforward to study using tensors and presents itself as a strong contender over other numerical methods.


  • Anosh Joseph (IISER Mohali)
    Title:     Complex Langevin Simulations of Dynamical Symmetry Breaking in IKKT Matrix Model
    Abstract:     In this talk, we report on the results of complex Langevin simulations of the IKKT matrix model. This model is conjectured to be a nonperturbative formulation of superstring theory in ten dimensions. Dynamical compactification of extra dimensions can be realized via spontaneous breaking of the model's SO(10) rotational symmetry. The phase of the Pfaffian in this model is inherently complex and thus can make Monte Carlo simulations unreliable. The complex Langevin method can handle wild fluctuations in the phase of the Pfaffian and give reliable results. Our preliminary simulation results point to dynamical symmetry breaking in the IKKT model.


  • Rak-Kyeong Seong (UNIST)
    Title:     Machine Learning Calabi-Yau Volumes
    Abstract:     The talk will give an overview of our work from 2017 which introduced machine learning techniques in string theory. This work made use of standard machine learning techniques, including convolutional neural networks (CNN), in order to find new formulas for the minimum volume of Sasaki-Einstein manifolds corresponding to toric Calabi-Yau 3-folds. These geometries, by the AdS/CFT correspondence, relate to a large class of 4d N=1 supersymmetric gauge theories. The R-charges of the dual gauge theories are known to be related to the minimum volumes of the corresponding Sasaki-Einstein manifolds. In this talk, we will review the process of volume minimization and give a short overview on ongoing work.


  • David Schaich (University of Liverpool)
    Title:     Numerical methods in lattice supersymmetry
    Abstract:     Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems, which has proven crucial to the study of quantum chromodynamics among many other theories. Lattice investigations of supersymmetric field theories have a long history but often struggle due to the interplay of supersymmetry with the lattice discretization of space-time. I will discuss a way around these difficulties for d-dimensional supersymmetric Yang--Mills (SYM) theories with at least 2^d supercharges, which include the case of superconformal N=4 SYM in 3+1 dimensions. With a focus on the numerical methods employed, I will review some highlights of the lattice formulation and survey a selection of results from recent and ongoing numerical studies, including tests of holographic dualities.

May 19 (Thu)


  • Piotr Sierant (ICFO)
    Title:     POLFED - a new diagonalization approach to study non-equilibrium phenomena
    Abstract:     I will describe polynomially filtered exact diagonalization (POLFED) method of computing eigenvectors of large sparse matrices at arbitrary energies - a task that often arises when studying non-equilibrium phenomena in quantum many-body systems. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale much better with system size than in the state-of-the-art shift-invert approach, while the total CPU time used by the two methods is similar. Also, the performance of POLFED is not severly impeded when the the number of non-zero elements in the matrix is increased allowing to efficiently study models with long-range interactions. A straightforward modification allows POLFED to investigate spectra of large Floquet unitary operators. I will demonstrate the potential of POLFED examining many-body localization transition in 1D interacting quantum spin-1/2 chains.


  • Snir Gazit (Hebrew University)
    Title:     Unconventional criticality and Fermi-surface reconstruction without symmetry breaking in a simple lattice model of gauge and matter fields.
    Abstract:     Gauge theories play a central role in the theoretical description of unconventional phases of matter that go beyond the standard paradigms of quantum statistical mechanics. While in high-energy physics, gauge fields correspond to fundamental particles, in condensed matter theory they are typically emergent and are invoked as an effective description of the low-energy degrees of freedom. Notable examples include spin-liquids, doped Mott insulators, and the fractional Hall effect, among others. In my talk, I will present a sign-problem free quantum Monte Carlo study of a lattice model hosting 'orthogonal' fermions coupled to an Ising-Higgs gauge theory. Our model provides a simple yet highly non-trivial example of electron fractionalization, which, crucially, remains numerically tractable. We uncover a particularly rich phase diagram arising from strong correlations between gauge and matter fields. In particular, we find that in the background of pi-flux lattice an orthogonal semi-metal (OSM) forms with gapless Dirac fermion excitations. With the tuning of parameters, the OSM undergoes a confinement transition, in which symmetry breaking and confinement are coincident. We construct a field-theoretical description of the transition involving condensation of a matrix Higgs field. The critical theory is predicted to sustain emergent and enlarged local (gauge) and global symmetries. We provide numerical evidence supporting this prediction. We also find that the physical (gauge-neutral) spectral function in the OSM phase comprises four fermion pockets, which smoothly evolve to a 'large' Fermi surface upon approach to a Fermi liquid phase. The reconstruction of the Fermi surface does not involve any form of translational symmetry breaking, in violation of the Luttinger sum rule.

May 20 (Fri)


  • Masazumi Honda (Kyoto University)
    Title:     Digital quantum simulation of higher-charge Schwinger model with topological term
    Abstract:     I am going to talk about application of quantum computation to numerical simulation of quantum field theory. Specifically we implement a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on 1+1 dimensional quantum electrodynamics with a topological term and a charge-q Dirac fermion known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum.

Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime.

We also study a potential between heavy charged particles and see that the potential changes its qualitative behavior as changing parameters: it shows confinement, screening and an exotic behavior called negative tension behavior in which particles with opposite charges repel with each other.

Refs:

[1] B.Chakraborty, M. Honda, T. Izubuchi, Y. Kikuchi and A. Tomiya, arXiv:2001.00485

[2] M. Honda, E. Itou, Y. Kikuchi, L. Nagano and T. Okuda, arXiv:2105.03276

[3] M. Honda, E. Itou, Y. Kikuchi and Y. Tanizaki arXiv:2110.14105


  • Ryo Hanai (APCTP)
    Title:     Nonreciprocal phase transitions
    Abstract: