Variational optimization with infinite projected entangled-pair states

Corboz, Philippe

doi:10.1103/physrevb.94.035133

Cited by 193 publications

(227 citation statements)

References 68 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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“…Therefore the method is very promising for future applications using PEPS. When we finalize the work, we get to know that variational optimization methods including the gradient method, 40,41 have been applied to optimize infinite PEPS wave functions where the gradients are calculated via direct contractions. It has also been shown that variational results are better than the best known full update results, consistent with our findings.…”

Section: Benchmark Resultsmentioning

confidence: 99%

Gradient optimization of finite projected entangled pair states

et al. 2017

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The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension D, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems. The optimization of the ground state using imaginary time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that combining the imaginary time evolution method with simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to D=10 without resorting to any symmetry. Benchmark tests of the method on the J1-J2 model give impressive accuracy compared with exact results.

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“…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]. In particular, for some models the PEPS framework can already compete with state-of-the-art results of Monte-Carlo simulations [103].…”

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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Variational optimization with infinite projected entangled-pair states

Cited by 193 publications

References 68 publications

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

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

Gradient optimization of finite projected entangled pair states

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

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