Tensor networks for gauge field theories

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of (1+1)-dimensional systems. In this proceeding we use MPS to determine the elementary excitations of the Schwinger model in the presence of an electric background field. We obtain an estimate for the value of the background field where the one-particle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.Comment: Proceeding of talk presented at the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japan; Proceeding of talk presented at The European Physical Society Conference on High Energy Physics, 22-29 July 2015, Vienna, Austria (PoS(EPS-HEP2015)375

Matrix product states for Hamiltonian lattice gauge theories

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.Comment: presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23 - 28 June 2014, New York, US

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Real-time simulation of the Schwinger effect with Matrix Product States

Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of local observables can be explained from the single-particle excitations of the quenched Hamiltonian. For large quenches damped oscillations are found and comparison of the late time behavior with the appropriate Gibbs states seems to give some evidence for the onset of thermalization. Finally, the MPS real-time simulations are explicitly compared with the semi-classical approach and, as expected, agreement is found in the limit of large quenches.Comment: Small changes, matching its published versio

Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED 2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field

Matrix product states for gauge field theories

The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study non-equilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.Comment: expanded discussion on real-time evolution, matching the published versio

Scaling hypothesis for matrix product states

We study critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theories. The critical point, exponents, and central charge are determined by optimizing them to obtain a data collapse. We benchmark this method by studying critical Ising and Potts models, where we also obtain a scaling Ansatz for the correlation length and entanglement entropy. The formulation of those scaling functions turns out to be crucial for studying critical quantum field theories on the lattice. For the case of lambda phi(4) with mass parameter mu(2) and lattice spacing a, we demonstrate a double data collapse for the correlation length delta xi(mu, lambda, D) = (xi) over tilde((alpha - alpha(c))(delta/a)(-1/nu)) with D the bond dimension, delta the gap between eigenvalues of the transfer matrix, and alpha(c) = mu(2)(R)/lambda the parameter which fixes the critical quantum field theory

Gauging quantum states: from global to local symmetries in many-body systems

We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration free gauge theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z2 gauge theory with Higgs matter.Comment: restructured to better reflect the general and PEPS-specific part, added supplementary material on injectivity in PEP

Challenges in transnational research programming: the role of NETWATCH

For Europe to meet the dual objectives of increased competitiveness and addressing societal challenges, joining efforts at all levels in Research and Innovation is high on the policy agenda. The EU can play a role in fostering and facilitating increased collaboration. The NETWATCH information platform on transnational collaboration is among the tools available to support this role. This brief explores the current use and future potential of NETWATCH and other related platforms in guiding and monitoring transnational R&I programming towards increased societal impact and competitiveness. It proposes ways to make better use of existing data, as well as avenues for future development.JRC.J.2-Knowledge for Growt

Measuring progress in transnational coordination of research programming in Europe

Cooperation in the EU between Member States and with Associated Countries on national public research programming has received a lot of attention in recent years, and will continue to do so under Europe 2020. This NETWATCH Policy Brief looks at the current policy context and rationales for transnational coordination of research programming, and aims to measure progress made so far in doing so. It looks both at coordination of public national research budgets and at cooperation between nations under the framework programmes, Horizon 2020 and Cohesion policy.JRC.J.2-Knowledge for Growt