Infinite matrix product states versus infinite projected entangled-pair states on the cylinder: A comparative study

Iregui, Juan Osorio; Troyer, Matthias; Corboz, Philippe

doi:10.1103/physrevb.96.115113

Cited by 9 publications

(7 citation statements)

References 56 publications

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“…Finally, we also compare variational ground state energies for the S = 1/2 Heisenberg antiferromagnet on a cylinder with results from Ref. 44 and 55. We have already seen in Fig.…”

Section: Comparison With Idmrg and Itebdmentioning

confidence: 92%

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Variational optimization algorithms for uniform matrix product states

et al. 2018

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We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform Matrix Product State algorithm (VUMPS) with infinite Density Matrix Renormalization Group (IDMRG) and with infinite Time Evolving Block Decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long range interactions and also for the simulation of two dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

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“…Finally, we also compare variational ground state energies for the S = 1/2 Heisenberg antiferromagnet on a cylinder with results from Ref. 44 and 55. We have already seen in Fig.…”

Section: Comparison With Idmrg and Itebdmentioning

confidence: 92%

“…also done in Ref. 44), we map the model onto a one-dimensional chain following a sawtooth path along the cylinder, such that the longest range spin-spin interactions are over W sites. We take the energies obtained from Loop QMC for several cylinder circumferences W presented in Table I in Ref.…”

Section: A Modelsmentioning

confidence: 99%

Variational optimization algorithms for uniform matrix product states

et al. 2018

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“…1(b)) extracts exactly the degrees of freedom that is in charge of the entanglement between one qudit block and its neighboring blocks. Following the spirit of the infinite-tensornetwork ansatz [26,[30][31][32], we represent a fixed-point…”

Section: Entanglement-renormalization Fixed Pointsmentioning

confidence: 99%

A new realization of the long-range entanglement: fractality replacing the topological order

Wang¹

2022

Preprint

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Quantum matter with fractal geometry has been recently observed and studied in experiments. The fractal self-similarity and the fractional nature of the spatial dimension in such systems suggest exotic quantum order lying beyond paradigms developed in integer dimension. However, the existence of such uncomprehended novelty is still to be established in terms of quantum states with nontrivial many-body entanglement. To lay a foundation for exploring such states and to provide example that demonstrates such novelty, we study many-body entanglement patterns in entanglement-renormalization fixed points of qudit systems with Sierpiński lattice geometry, and introduce corresponding toy models. We show that the interplay between entanglement and selfsimilarity can be realized in fixed-point states with well-defined self-similar entanglement patterns. These fixed-point states exhibit distinct orders and are all given by single tensors as solutions to a scale invariance equation. In particular, we prove that an example of fixed-point state possesses long-range entanglement, i.e., it is short-range correlated but cannot be completely disentangled through constant-depth local quantum circuit. While the existence of long-range entanglement implies topological order in 2D and is disproved in 1D, our example proves the coexistence between long-range entanglement and fractality, a paradigm in fractional dimension. We show that such long-range entanglement pattern cannot be read as an extension of topological order, but rather exhibits novel quantum ordering inherent in fractional dimension, an evidence of new paradigm describing long-range entanglement.

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“…They originated from the understanding that the density matrix renormalization group (DMRG) technique could be recast in a variational formulation by means of matrix product states (MPS) [6][7][8]. This stimulated the further development of such a framework in the last decade, extending the TN paradigm to encompass higher dimensionality [9][10][11][12][13][14], peculiar geometries [15,16], directly addressing the thermodynamical limit [17][18][19], as well as the continuum [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Loop-free tensor networks for high-energy physics

Montangero

Rico

Silvi

2021

Phil. Trans. R. Soc. A.

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This brief review introduces the reader to tensor network methods, a powerful theoretical and numerical paradigm spawning from condensed matter physics and quantum information science and increasingly exploited in different fields of research, from artificial intelligence to quantum chemistry. Here, we specialize our presentation on the application of loop-free tensor network methods to the study of high-energy physics problems and, in particular, to the study of lattice gauge theories where tensor networks can be applied in regimes where Monte Carlo methods are hindered by the sign problem. This article is part of the theme issue ‘Quantum technologies in particle physics’.

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Infinite matrix product states versus infinite projected entangled-pair states on the cylinder: A comparative study

Cited by 9 publications

References 56 publications

Variational optimization algorithms for uniform matrix product states

Variational optimization algorithms for uniform matrix product states

A new realization of the long-range entanglement: fractality replacing the topological order

Loop-free tensor networks for high-energy physics

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