Automated construction of $U(1)$-invariant matrix-product operators from  graph representations

Paeckel, Sebastian; Köhler, Thorsten; Manmana, Salvatore R.

doi:10.21468/scipostphys.3.5.035

Cited by 19 publications

(23 citation statements)

References 26 publications

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“…Note that it appears useful for future studies to use a formulation of the algorithm in terms of matrix product operators, as, e.g., discussed in Refs. [28,73] and references therein, which speeds up the calculations.…”

Section: Density-matrix Renormalization Groupmentioning

confidence: 93%

Correlations and enlarged superconducting phase of t−J⊥ chains of ultracold molecules on optical lattices

Manmana¹,

Möller²,

Gezzi³

et al. 2017

Phys. Rev. A

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We compute physical properties across the phase diagram of the t-J ⊥ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component J z of the spin-spin interaction and the charge component V are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.

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Section: Density-matrix Renormalization Groupmentioning

confidence: 93%

Correlations and enlarged superconducting phase of t−J⊥ chains of ultracold molecules on optical lattices

Manmana¹,

Möller²,

Gezzi³

et al. 2017

Phys. Rev. A

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“…The operator-valued matricesÂ,B,Ĉ andD then define the recursion relations to iteratively build the complete operatorĤ. This picture directly leads to a construction of MPOs based on finite-state machines (FSM) [61,63]. In analogy to matrix-product states with bonds m j and a maximal bond dimension m, the bonds of matrix-product operators are labelled by w j with the maximal bond dimension denoted by w. Figure 4: Left (Right) normalized tensor A j (red, right-pointing triangle) (B j (green, left-pointing triangle)) contracted with its adjoint resulting in an identity.…”

Section: Matrix-product Operators (Mpo)mentioning

confidence: 99%

Time-evolution methods for matrix-product states

et al. 2019

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Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W I,II method, the global Krylov method, the local Krylov method and the one-and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

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“…To derive the form of the matrices for a more complicated Hamiltonian, it can be useful to view the MPO as a finite state machine [63,64]. Using this concept, the generation of an MPO for models with finite-range (two-body) interactions is automated in TeNPy [1].…”

Section: Matrix Product Operators (Mpo)mentioning

confidence: 99%

Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

Hauschild

Pollmann

2018

SciPost Phys. Lect. Notes

445

291

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Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

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Automated construction of $U(1)$-invariant matrix-product operators from graph representations

Cited by 19 publications

References 26 publications

Correlations and enlarged superconducting phase of t−J⊥ chains of ultracold molecules on optical lattices

Correlations and enlarged superconducting phase of t−J⊥ chains of ultracold molecules on optical lattices

Time-evolution methods for matrix-product states

Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

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