Finite-density phase diagram of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mi>d</mml:mi></mml:math>non-abelian lattice gauge theory with tensor networks

Silvi, Pietro; Rico, E.; Dalmonte, Marcello; Tschirsich, Ferdinand; Montangero, Simone

doi:10.22331/q-2017-04-25-9

Cited by 69 publications

(54 citation statements)

References 82 publications

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“…The model has also been studied at non-zero temperature [4,[33][34][35][36][37], non-zero chemical potential [30,31,38] and for real-time problems [27,39]. In addition, quantum link models [40,41] and non-Abelian gauge models have been explored with the MPS approach [42][43][44][45][46][47]. Besides MPS, also tensor network renormalization techniques [48][49][50] have been very successfully employed to study properties of gauge theories in 1+1 dimensions and recently even in a simple (2+1)-dimensional gauge theory [51].…”

Section: Introductionmentioning

confidence: 99%

Topological vacuum structure of the Schwinger model with matrix product states

2020

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We numerically study the single-flavour Schwinger model in the Hamiltonian formulation with a topological θ-term corresponding to a constant electric background field. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial θ-dependence of several lattice and continuum quantities. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle θ, thus respecting CP invariance, while lattice artifacts still depend on θ. We also confirm that negative masses can be mapped to positive masses by shifting θ → θ + π due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping.

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Section: Introductionmentioning

confidence: 99%

Topological vacuum structure of the Schwinger model with matrix product states

2020

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“…Ever since the formulation of Density Matrix Renormalization Group [7] in terms of MPS, the number of algorithms for quantum many-body systems has increased rapidly. Recently, MPS have also been successfully applied to lattice gauge theories [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

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confidence: 99%

Real-time simulation of the Schwinger effect with matrix product states

et al. 2017

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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 compared with results from real-time lattice gauge theory which are expected to agree in the limit of large quenches.

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“…the screening of these charges. Another study of the SU (2) gauge theory with tensor networks was performed by Silvi et al [338] in 2016, with the aim of investigating the finite density phase diagram in the plane filling vs. coupling. The authors used the quantum link formulation to achieve finite-dimensional link Hilbert space while preserving the exact gauge symmetry.…”

Section: Non-abelian Su (2) and Su (3) Gauge Theoriesmentioning

confidence: 99%

Review on novel methods for lattice gauge theories

2020

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Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem.In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

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Finite-density phase diagram of a(1+1)−dnon-abelian lattice gauge theory with tensor networks

Cited by 69 publications

References 82 publications

Topological vacuum structure of the Schwinger model with matrix product states

Topological vacuum structure of the Schwinger model with matrix product states

Real-time simulation of the Schwinger effect with matrix product states

Review on novel methods for lattice gauge theories

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