|Date|| Seminars 2017 (Go to Seminars 2016, Seminars 2015, Seminars 2014, and earlier therein)
|09.01.2017||Bipartite charge fluctuations in Z_2 topological insulators and superconductors
Invited speaker: Loïc Herviou (Ecole Polytechnique, ENS)
Bipartite charge fluctuations (BCF) have been introduced to provide an experimental indication of many-body entanglement.They are a very efficient and useful tool to characterize phase transitions in a large variety of charge-conserving models in one and two dimensions In this seminar, we study the BCF in generic one- and two-dimensional Z_2 (topological) models such as the Kitaev chain, spin-orbit insulators, the graphene and the Haldane model, where the charge we observe is no longer conserved. In one-dimension, we demonstrate that at phase transitions characterized by a linear dispersion, the BCF probe the change in a winding number that allows to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a sub-dominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and a characteristic of the critical model. In two dimensions, a similar structure appears. While the area term no longer reveal directly the phase transition, a subdominant logarithmic term is still present. Similarly to the entanglement entropy, it depends on the exact shape of the considered region, with contributions of the corner of the regions only.
|25.01.2017||Approaching non-Abelian Lattice Gauge Theories with Tensor Networks
In recent years the Tensor Network approach to lattice gauge theories has proven itself as promising alternative to the conventional Monte Carlo methods widely used. In contrast to Monte Carlo simulations, numerical methods based on Tensor networks do not suffer from the sign problem, thus allowing to address problems and parameter regimes which are inaccessible with Monte Carlo. However, even for for the simplest non-Abelian gauge models with dynamical fermions, the computational effort typically grows quickly. Hence, current Tensor Network simulations for non-Abelian models are rather limited.
In this talk I will address the case of a SU(2) lattice gauge theory. I will show how, starting from a basis of color neutral states, the gauge field for systems on finite lattices with open boundary conditions can be integrated out, thus greatly reducing the degrees of freedom. While this formulation is completely general, it trivially allows to truncate the maximum color-electric flux in the system, thus making it particularly suitable for a Tensor Network approach. As a proof of principle I will present numerical results for the low lying spectrum obtained with Matrix Product States for a family of truncated SU(2) models.
|01.02.2017||Decay of correlations in systems of fermions with long-range interactions at non-zero temperature
We study correlations in fermionic systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anti-commuting operators based on long-range Lieb-Robinson type bounds. Our result shows that correlations between such operators in fermionic long-range systems of spatial dimension $D$ with at most two-site interactions decaying algebraically with the distance with an exponent $\alpha \geq 2\,D$, decay at least algebraically with an exponent arbitrarily close to $\alpha$. Our bound is asymptotically tight, which we demonstrate by numerically analyzing density-density correlations in a 1D quadratic (free, exactly solvable) model, the Kitaev chain with long-range interactions. Away from the quantum critical point correlations in this model are found to decay asymptotically as slowly as our bound permits.
|08.02.2017||An introduction to Variational Monte-Carlo
Variational Monte-Carlo methods are used to determine the energy of a wave function and to optimize its parameters in order to approximate the ground state of a many-body quantum system. In this talk I will give a general introduction to Variational Monte-Carlo. Starting from the early days of Monte-Carlo integration I will explain how these methods can be used to compute energies of wave functions. I will then give an overview of modern methods to optimize the energy of a wave function with many parameters.
|15.02.2017||Simulating non-Equilibrium systems with Matrix Product States
Understanding out of equilibrium remains a challenge for classical and quantum systems. There is no general non-equilibrium statistical mechanics framework to resort to, if one is interested in the statistical properties of observables in far from equilibrium situations. The theory of large deviations can fill this gap in some cases and Tensor Networks are one possibility to explore this problem from a numerical side. Matrix Product States can capture the properties of non-equilibrium stationary states of many classical and quantum models. On Wednesday I will discuss how people have used these techniques for the simplest problem of particle hopping on a 1D lattice.
|21.02.2017 at 14:00||Dissipation induced topological states: A recipe
Invited speaker: Moshe Goldstein (Tel-Aviv University)
It has recently been realized that driven-dissipative dynamics, which usually tends to destroy subtle quantum interference and correlation effects, could actually be used as a resource. By proper engineering of the reservoirs and their couplings, one may drive a system towards a desired quantum-correlated steady state, even in the absence of internal Hamiltonian dynamics.
An intriguing class of quantum phases is characterized by topology, including the quantum Hall effect and topological insulators and superconductors. Which of these noninteracting topological states can be achieved as the result of purely dissipative Lindblad-type dynamics? Recent studies have only provided partial answers to this question.
In this talk I will present a general recipe for the creation, classification, and detection of states of the integer quantum Hall and 2D topological insulator type as the outcomes of coupling a system to reservoirs, and show how the recipe can be realized with ultracold atoms and other quantum simulators. The mixed states so created can be made arbitrarily close to pure states. I will discuss ways to extend this construction to other topological phases, including non-Gaussian ones, such as fractional quantum Hall state.
|01.03.2017 at 14:00||Characterizing many-body states at finite temperature via a Klein twist
Invited speaker: Hong-Hao Tu (Ludwig-Maximilians-Universität - München )
In this talk, I will describe an ongoing work on how universal data for distinguishing different phases may be extracting from thermal states of quantum many-body systems. This approach relies on a Klein bottle partition function (defined by twisting the usual partition function in imaginary-time axis) and is relevant for situations where non-chiral conformal field theories govern the bulk or edge physics (e.g. 1d critical states and 2d time-reversal invariant topological insulators). Benchmark results will be provided for several 1d critical models.
|02.03.2017 at 11:30||Majorana quasi-particles from angular momentum conservation
Invited speaker: Fernardo Iemini (International Centre for Theoretical Physics - Trieste, Italy)
We show how angular momentum conservation can stabilise a quasi-topological phase of matter supporting Majorana qausi-particles as edge modes. Differently from typical scenarios, where such quasi-particles require the presence of superconductivity, we investigate orbital SU (2) × SU (2) Hubbard models in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional models. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated with numerical simulations. Our results pave the way toward the observation of Majorana edge modes with Alkaline-earth-like fermions in optical lattices, where the basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been observed over the last two years.
|08.03.2017||Almost Conserved Local Operators in MBL systems
Long time dynamics of non-integrable systems holds the key to fundamental questions (thermalization). Analytical tools can only apply to particular cases (integrable models, perturbative regimes). Numerical simulations, limited in time, have found evidence of different time scales. A new numerical technique for constructing slowly evolving local operators was introduced by Kim et al. in Phys. Rev. E 92, 012128 (2015). Those operators have a small commutator with the Hamiltonian and they might give rise to long time scales. In this work, we apply this technique to the many body localization problem. We show that this method can not only signal the difference between the ergodic and localized phases, but it is also sensitive to the presence of the Griffith region between both.
|15.03.2017||Efficient representation of fully many-body localized systems using tensor networks
Invited speaker: Thorsten Wahl (Oxford University)
Many-body localization (MBL) is currently an intensely studied topic and characterized by the fact that certain strongly disordered systems fail to thermalize. For sufficiently strong disorder in one dimension, all eigenstates of MBL systems fulfill the area law of entanglement. This makes tensor network states ideally suited to represent such fully many-body localized systems. Building on the ansatz proposed in Phys. Rev. B 94, 041116(R) (2016), I will present a tensor network that is able to capture the full set of eigenstates of such MBL systems efficiently: For a given system size, local observables can be approximated with an error that decreases as an inverse polynomial of the computational cost, which is an exponential improvement over the previous ansatz. If the system size is increased, the computational cost needs to grow only linearly with the system size in order to keep the accuracy fixed. The technique turns out to be highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the dynamical phase transition. Finally, the power of the technique is demonstrated on systems of 72 sites, where clear signatures of the phase transition can be seen.
|22.03.2017||A generalisation of the injecitvity condition for PEPS
Projected Entangled Pair States (PEPS) is an ansatz believed to be suitable for analytical and numerical investigation of ground states of many-body Hamiltonians. To design a PEPS that admits certain (local) symmetries one has to understand when two different PEPS tensors give rise to the same state. This question in the full generality is however undecidable, it is therefore important to find relevant classes of tensors for which it can be answered. One such class is injcetive PEPS. Two injective PEPS describe the same state if and only if their tensors are related with a gauge transformation on the virtual space. Here we provide a generalisation of this class. This generalisation includes states that fail to be injective for purely geometrical reasons (so called corner problem). We show under which condition can two such states be equal. We also show that symmetries give rise to invertible Matrix Product Operators (MPO) on the boundary degrees of freedom. These MPOs can be used to assign an element of the third cohomology of the symmetry group to the state the same way as in the classification of the Symmetry Protected Topological (SPT) phases.
|23.03.2017 at 14:00||DMRG with Subspace Expansion on Symmetry-Protected Tensor Networks
Invited speaker: Claudius Hubig (Ludwig-Maximilians-Universität - München)
The Density Matrix Renormalisation Group when applied to matrix- product states is the method of choice for ground-state search on one-dimensional systems and still highly competitive even in unfavourable circumstances, such as critical systems and higher dimensions.
In this talk, I will discuss two separate methods which can be used to improve the computational efficiency of DMRG and related methods on matrix-product states and beyond. The first component is the implementation of both abelian and non-abelian symmetries in an entirely general way suitable also for higher-rank tensors as encountered in e.g. tree tensor network states. The second ingredient, the subspace expansion, allows for a fully single-site DMRG algorithm with favourable linear scaling in the local dimension of the tensor network. Even for common problems, this results in a considerable speed-up over the traditional two-site DMRG method or the density matrix perturbation approach for ground-state search at reduced algorithmic complexity. Additionally, the subspace expansion can potentially be used in a large set of other algorithms, such as the TDVP or the variational application of a matrix-product operator onto a matrix-product state.
|27.03.2017 at 11:30||Decoding Protocols for Classical Communication on Quantum Channels
Invited speaker: Matteo Rosati (Scuola Normale Superiore, Pisa, Italy )
I discuss the transmission of classical information via quantum carriers with focus on the decoding stage. While the optimal transmission rate and encoding have been well studied in the past providing viable solutions for free-space or optical-fiber communication, a practical decoder is still difficult to design. This is due to the requirement of performing joint measurements over several transmission modes and their difficult implementation. I approach the problem from several points of view presenting ideas for decoding algorithms and practical devices, especially for communication with coherent states of the electromagnetic field.
|29.03.2017||High-Fidelity Hot Gates for Generic Spin-Resonator Systems
Invited speaker: Martin Schütz (Harvard University)
We propose and analyze a high-fidelity hot gate for generic spin-resonator systems which allows for coherent spin-spin coupling, in the presence of a thermally populated resonator mode. Our scheme is non-perturbative, applies to a broad class of physical systems, including for example spins coupled to circuit-QED and surface acoustic wave resonators as well as nanomechanical oscillators, and can be implemented readily with state-of-the-art experimental setups. We provide and numerically verify simple expressions for the fidelity of creating maximally entangled states under realistic conditions.