Superfluid-to-Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation

Kohn, Lucas; Silvi, Pietro; Gerster, Matthias; Keck, Maximilian; Fazio, Rosario; Santoro, Giuseppe E.; Montangero, Simone

doi:10.1103/physreva.101.023617

Cited by 18 publications

(9 citation statements)

References 78 publications

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“…We verified the TDVP approach by comparing first to TEBD using a diagonal bath including interactions, and second to the exact solution in the non-interacting case for an off-diagonal bath. When finalizing this manuscript we became aware of an independent publication by Kohn et al [42], describing the TDVP applied to a TTN for periodic boundary conditions in a one-dimensional system.…”

Section: Resultsmentioning

confidence: 99%

Time dependent variational principle for tree Tensor Networks

Bauernfeind

Aichhorn

2020

SciPost Phys.

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We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same tensor network structure that encodes the state is available. Often, such a representation can be found also for long-range terms in the Hamiltonian. As an application we use TDVP for the Fork Tensor Product States tensor network for multi-orbital Anderson impurity models. We demonstrate that TDVP allows to account for off-diagonal hybridizations in the bath which are relevant when spinorbit coupling effects are important, or when distortions of the crystal lattice are present.arXiv:1908.03090v2 [cond-mat.str-el] 6 Sep 2019 SciPost Physics Submission method to calculate dynamical properties [21][22][23][24]. Approaches to perform the real-time evolution include, among others, the Time-dependent Density Matrix Renormalization Group (tDMRG) [25,26], the closely related Time Evolving Block Decimation (TEBD) [27,28] as well as the Time Dependent Variational Principle (TDVP) [29,30]. An in depth comparison of several time evolution algorithms performed in Ref. [31] came to the conclusion that while all approaches have strengths and weaknesses, TDVP is among the most reliable methods to perform the time evolution. While time evolution approaches for MPS are well established, much less has been done for general tensor networks. So far, mostly TEBD (and minor variations) have been used, for example for the MERA network [32], for PEPS [33] and for TTNs [9,17,18,34,35]. The advantage of TEBD is its relative simplicity, since it effectively boils down to a repeated application of short range operators obtained from a Suzuki-Trotter decomposition [36] of the full time-evolution operator. However, one of the major disadvantages of TEBD is that it can become difficult to implement for more complicated Hamiltonians, especially when long-range couplings are present. TDVP to some degree circumvents this problem by only demanding a Hamiltonian represented in the same tensor network structure as the state which is often easy to find. Additionally, TDVP in its single-site variant exactly respects conserved quantities of the Hamiltonian like energy or magnetization [30]. Although some works applied TDVP to more general tensor networks [37,38], it is not obvious how these algorithms work in detail and how it can be generalized. A more practical motivation for the formulation of TDVP for TTNs are Dynamical Mean-Field Theory (DMFT) calculations using the FTPS tensor network. So far, this approach has been used for so-called diagonal hybridizations only. On the other hand, real materials often exhibit off-diagonal hybridizations, which can for example come from spin-orbit coupling, or from distortions of the crystal lattice. For off-diagonal hybridizations, the TEBD approach used so far [18,19] is difficult to generalize and we hence choose to use TDVP in these situations. Although part of the motivatio...

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Section: Resultsmentioning

confidence: 99%

Time dependent variational principle for tree Tensor Networks

Bauernfeind

Aichhorn

2020

SciPost Phys.

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“…We carry out simulations using the 2-site version of the time-dependent variational principle (TDVP) [41][42][43][44], which, in combination with the matrix product operator representation of the Hamiltonian, allows us to deal with next-nearest neighbor interaction. Using TDVP, it would also be possible to simulate more complicated networks [39,45,46], which would be needed to split both spin degrees of freedom and empty/filled chains. Depending on the MPS ordering, we use bond dimensions between D = 150 and D = 1600 to reach convergence (see Appendix D) and a total truncated weight w t -the summed probability of discarded states -of w t = 10 −12 for the truncation of the MPS.…”

Section: Chain Mapping With Orthogonal Polynomialsmentioning

confidence: 99%

Quenching the Anderson impurity model at finite temperature: Entanglement and bath dynamics using matrix product states

Kohn,

Santoro

2021

Preprint

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We study the dynamics of the quenched Anderson model at finite temperature using matrix product states. Exploiting a chain mapping for the electron bath, we investigate the entanglement structure in the MPS for various orderings of the two chains, which emerge from the thermofield transformation employed to deal with nonzero temperature. We show that merging both chains can significantly lower the entanglement at finite temperatures as compared to an intuitive nearestneighbor implementation of the Hamiltonian. Analyzing the population of the free bath modes -possible when simulating the full dynamics of impurity plus bath -we find clear signatures of the Kondo effect in the quench dynamics.

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“…As a loop-free (or loop-less) TN, TTNs benefit from an extremely robust groundwork of algorithms, developed and refined over two decades, capable of performing the two standard tasks of (closed-system) quantum mechanics: (i) ground state search, and (ii) real-time evolution, corresponding respectively to the time-independent and time-dependent formulations of the Schrödinger equation, for a many-body lattice Hamiltonian H. Modern TTN numerical suites employ a generalization of DMRG for loop-less TNs in order to tackle the ground state search [27,72], while real-time dynamics is typically carried out by time-dependent variational principle (TDVP), originally designed for MPS [63,73], but allowing a natural generalization for loop-less TN [74,75].…”

Section: (B) Tree Tensor Networkmentioning

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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Superfluid-to-Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation

Cited by 18 publications

References 78 publications

Time dependent variational principle for tree Tensor Networks

Time dependent variational principle for tree Tensor Networks

Quenching the Anderson impurity model at finite temperature: Entanglement and bath dynamics using matrix product states

Loop-free tensor networks for high-energy physics

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