Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

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

doi:10.1016/j.aop.2016.08.008

Cited by 49 publications

(72 citation statements)

References 62 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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“…One can thus study the transition from the weak to the strong coupling regime as a function of k. This has the advantage of working with manifestly finite Hilbert spaces for finite k. As the dynamics is also adjusted to the k-level, it presents a far more elegant cut-off than truncating away all representation labels larger than some j max [116][117][118][119]. …”

Section: √λmentioning

confidence: 99%

“…This is important for numerical coarse graining techniques, such as tensor network algorithms for lattice gauge theories [51,52,[116][117][118][119]. The finiteness of such q-deformed models has also been used to investigate certain two-dimensional models, designed to reproduce key dynamical mechanisms of spin foams [46][47][48][49][50].…”

Section: √λmentioning

confidence: 99%

Cosmological Constant from Condensation of Defect Excitations

Dittrich

2018

Universe

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A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of (2 + 1)-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales. These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant. They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant. A similar construction is possible in four dimensions, in this case the curvature is concentrated along string-like defects and the states are vacua of the Crane-Yetter model. We will sketch applications for quantum cosmology and condensed matter.

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Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

Cited by 49 publications

References 62 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

Cosmological Constant from Condensation of Defect Excitations

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