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

Hauschild, Johannes; Pollmann, Frank

doi:10.21468/scipostphyslectnotes.5

Cited by 447 publications

(332 citation statements)

References 68 publications

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“…For finite systems, the entanglement entropy should increase with the bond dimension χ, which is the parameter that controls the truncation of the system as iDMRG is performed. 44 The results are shown in Fig. 4 for three representative values of the twist angle.…”

Section: Numerical Resultsmentioning

confidence: 99%

Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction

et al. 2019

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We investigate an antiferromagnetic spin-1 Heisenberg chain in the presence of Dyzaloshinskii-Moriya interactions (DMI) and an external magnetic field. We study the resulting spin chain using a combination of numerical and analytical techniques. Using DMRG simulations to determine the spectral gap and the entanglement spectrum, we map out the phase diagram as a function of magnetic field strength and DMI strength. We provide a qualitative interpretation for these numerical findings by mapping the spin-1 chain on a spin-1/2 ladder and using a bosonization approach.

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Section: Numerical Resultsmentioning

confidence: 99%

Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction

et al. 2019

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“…Here we perform DMRG simulations on a 8×6 cylinder, using the TeNPy package [46], to search for similar signatures of geometric strings in the ground state of the t − J model with exactly one hole, |Ψ 1h . To generate snapshots {|α n } of the wavefunction, we employ Metropolis Monte Carlo sampling of Fock basis states |α with one hole and calculate the required overlap | α|Ψ 1h | 2 using the matrix product state formalism.…”

Section: B Parton Picture: Spinons Chargons and Stringsmentioning

confidence: 99%

Microscopic spinon-chargon theory of magnetic polarons in the t−J model

2019

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The interplay of spin and charge degrees of freedom, introduced by doping mobile holes into a Mott insulator with strong anti-ferromagnetic (AFM) correlations, is at the heart of strongly correlated matter such as high-Tc cuprate superconductors. Here we capture this interplay in the strong coupling regime and propose a trial wavefunction of mobile holes in an AFM. Our method provides a microscopic justification for a class of theories which describe doped holes moving in an AFM environment as meson-like bound states of spinons and chargons. We discuss a model of such bound states from the perspective of geometric strings, which describe a fluctuating lattice geometry introduced by the fast motion of the chargon. This is demonstrated to give rise to short-range hidden string order, signatures of which have recently been revealed by ultracold atom experiments. We present evidence for the existence of such short-range hidden string correlations also at zero temperature by performing numerical DMRG simulations. To test our microscopic approach, we calculate the ground state energy and dispersion relation of a hole in an AFM, as well as the magnetic polaron radius, and obtain good quantitative agreement with advanced numerical simulations at strong couplings. We discuss extensions of our analysis to systems without long range AFM order to systems with short-range magnetic correlations.

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“…The situation in the spin chain, we argue here, is slightly more favorable, which is one of the motivations for investigating T-W scaling in this quantum system. While the Hilbert space size naively grows exponentially fast, powerful variational techniques such as DMRG [33] are able to find the ground state with very good accuracy for large enough R. Efficient DMRG libraries able to implement continuous symmetries are now available in several programming languages (including Python [34] and C++ [35]), which simplifies our task considerably in the XXZ spin chain. The simulations shown below were performed using the C++ ITensor library [35].…”

Section: Numerical Checksmentioning

confidence: 99%

Free fermions at the edge of interacting systems

Stéphan

2019

SciPost Phys.

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We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

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

Cited by 447 publications

References 68 publications

Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction

Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction

Microscopic spinon-chargon theory of magnetic polarons in the t−J model

Free fermions at the edge of interacting systems

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