Fermionic projected entangled pair states and local<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si86.gif" display="inline" overflow="scroll"><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>gauge theories

Zohar, Erez; Burrello, Michele; Wahl, Thorsten B.; Cirac, J. I.

doi:10.1016/j.aop.2015.10.009

Cited by 70 publications

(126 citation statements)

References 85 publications

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“…On the other hand, it is a major goal to extend this type of real-time simulation technique to more than one spatial dimension using projected entangled pair states (PEPS) [4]. The major progress on PEPS algorithms in the last decade [93][94][95][96][97][98][99][100][101][102] in combination with recent promising PEPS and TNS results for higher-dimensional gauge theories [103][104][105][106][107] makes us confident that this will be realized in the foreseeable future.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

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

et al. 2017

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“…The generalization of MPS to higher dimensions are the Projected Entangled-Pair States (PEPS) [91]. Although some interesting studies of gauge theories with PEPS have appeared [92][93][94][95][96], at present, the need for a large number of variational freedom when approaching the continuum limit, is still hindering a truly variational study of gauge field theories [97]. Fortunately, in the last years the PEPS methods have significantly improved [98][99][100][101][102][103][104][105][106][107].…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2017

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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, oneflavour QED2, 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.

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“…[7,8,9,10,11,12]. For higher dimensions different gauge invariant TNS constructions have also been developed [13,14,15,16] with some first numerical applications on simple gauge theories.…”

Section: Introductionmentioning

confidence: 99%

“…[7,8,9,10,11,12]. For higher dimensions different gauge invariant TNS constructions have also been developed [13,14,15,16] with some first numerical applications on simple gauge theories.Here we continue our research on the Schwinger model [8,9,10] by investigating the one-particle spectrum in the presence of an electric background electric field gα. For α = 1/2 something interesting happens.…”

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confidence: 99%

Tensor networks for gauge field theories

Buyens¹,

Haegeman²,

Verstraete³

et al. 2016

Proceedings of the European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2015)

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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 oneparticle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.The European Physical Society Conference on High Energy Physics 22-29 July 2015 Vienna, Austria * Speaker. PoS(EPS-HEP2015)375TN for gauge field theories K. Van Acoleyen IntroductionIn a quantum many body system the dimension of the Hilbert space increases exponentially with the number of sites. This makes any attempt of solving a realistic system using exact diagonalization impossible. Fortunately, research on entanglement showed that the low energy states of local gapped Hamiltonians live in a tiny corner of the Hilbert space. Because they dominate the behavior of condensed matter systems at low temperatures, it indeed makes sense to focus on the low energy states. Also for quantum field theories, independent of whether they are strongly coupled or weakly coupled, the low energy regime is of interest The tensor network states (TNS) [1] are a variational class of states living in this tiny corner. Ideally, the number of parameters of these states is small and expectation values of local quantities can be computed efficiently in the number of sites in the system. In one spatial dimension the most famous example are the matrix product states (MPS). It is rigorously proven that they can efficiently approximate the low-energy states of a local gapped Hamiltonians [2]. The many successful simulations of many-body systems using MPS in the last decade showed that this result is not only of theoretical interest. Furthermore, as MPS are formulated in the Hamiltonian framework, they allow the difficult simulation of out-of-equilibrium physics [3,4]. In the last years MPS has proven to be powerful for gauge theories, e.g. [5,6]. In particular for the massive Schwinger model, QED 2 with one flavor, different groups considered MPS simulations, e.g. [7,8,9,10,11,12]. For higher dimensions different gauge invariant TNS constructions have also been developed [13,14,15,16] with some first numerical applications on simple gauge theories.Here we continue our research on the Schwinger model [8,9,10] by investigating the one-particle spectrum in the presence of an electric background electric field gα. For α = 1/2 something interesting happens. As the fermion mass increases there will be a phase transition around (m/g) c ≈ 0.33 related to the spontaneous breaking of the CT-symmetry [7,17,18]. The ground state is degenerate for m/g > (m/g) c and kinks 'connecting' the two vacua arise. This is different from the spectrum in the case of a zero backgroun...

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Fermionic projected entangled pair states and localU(1)gauge theories

Cited by 70 publications

References 85 publications

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

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

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

Tensor networks for gauge field theories

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