Improved matrix product operator renormalization group: application to the <i>N</i>-color random Ashkin–Teller chain

Chatelain, Christophe

doi:10.1088/1742-5468/ab3785

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…In Ref. [41] selections of blocks for the renormalization were adjusted to the specific models under consideration; in Ref. [42] optimization using variational energy minimization after coarse-graining was introduced, as an extension of tSDRG and the multiscale entanglement renormalization ansatz (MERA) [43,44].…”

Section: Summary and Discussionmentioning

confidence: 99%

Tensor network renormalization group study of spin-1 random Heisenberg chains

2020

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We use a tensor network strong-disorder renormalization group (tSDRG) method to study spin-1 random Heisenberg antiferromagnetic chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase known as the Haldane phase. Here we consider disordered chains with random couplings, in which the Haldane gap closes in the strong disorder regime. As the randomness strength is increased further and exceeds a certain threshold, the random chain undergoes a phase transition to a critical random-singlet phase. The strong-disorder renormalization group method formulated in terms of a tree tensor network provides an efficient tool for exploring ground-state properties of disordered quantum many-body systems. Using this method we detect the quantum critical point between the gapless Haldane phase and the randomsinglet phase via the disorder-averaged string order parameter. We determine the critical exponents related to the average string order parameter, the average end-to-end correlation function and the average bulk spin-spin correlation function, both at the critical point and in the random-singlet phase. Furthermore, we study energy-length scaling properties through the distribution of energy gaps for a finite chain. Our results are in closer agreement with the theoretical predictions than what was found in previous numerical studies. As a benchmark, a comparison between tSDRG results for the average spin correlations of the spin-1/2 random Heisenberg chain with those obtained by using unbiased zero-temperature QMC method is also provided.

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Section: Summary and Discussionmentioning

confidence: 99%

Tensor network renormalization group study of spin-1 random Heisenberg chains

2020

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“…Despite the fact that the inter-chain coupling flows towards an infinite value during renormalization, the critical behavior is still in the RTIM universality class along these two lines 15 . In the case N ≥ 3, the pure Ashkin-Teller chain undergoes a first-order phase transition, as the Potts model with q ≥ 4, which becomes continuous in presence of disorder 14,[17][18][19][20] . The critical behavior is in the RTIM universality class at weak inter-chain coupling but seems to be governed by a distinct IDFP at stronger inter-chain coupling 18 .…”

Section: Introductionmentioning

confidence: 99%

Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models

Anfray,

Chatelain

2021

Preprint

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The random q-state quantum Potts model is studied on hypercubic lattices in dimensions 2 and 3 using the numerical implementation of the Strong Disorder Renormalization Group introduced by Kovacs and Iglói [Phys. Rev. B 82, 054437 (2010)]. Critical exponents ν, d f and ψ at the Infinite Disorder Fixed Point are estimated by Finite-Size Scaling for several numbers of states q between 2 and 50. When scaling corrections are not taken into account, the estimates of both d f and ψ systematically increase with q. It is shown however that q-dependent scaling corrections are present and that the exponents are compatible within error bars, or close to each other, when these corrections are taking into account. This provides evidence of the existence of a super-universality of all 2D and 3D random Potts models.

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“…The traditional block-spin renormalization for critical points corresponds to scale-invariant Tree-Tensor-States, and has been improved via the multi-scale-entanglement-renormalization-ansatz (MERA) [21,22], where 'disentanglers' between blocks are introduced besides the block-coarse-graining isometries already present in Tree-Tensor-States. Finally in the field of disordered spin chains, the Strong Disorder Renormalization approach (see the reviews [23,24]) has been reformulated either as a Matrix-Product-Operator-Renormalization or as a self-assembling Tree-Tensor-Network, and various improvements have been proposed [25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder

Monthus

2020

Preprint

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The simplest Tree-Tensor-States (TTS) respecting the Parity and the Time-Reversal symmetries are studied in order to describe the ground states of Long-Ranged Quantum Spin Chains with or without disorder. Explicit formulas are given for the one-point and two-point reduced density matrices that allow to compute any one-spin and two-spin observable. For Hamiltonians containing only one-body and two-body contributions, the energy of the TTS can be then evaluated and minimized in order to obtain the optimal parameters of the TTS. This variational optimization of the TTS parameters is compared with the traditional block-spin renormalization procedure based on the diagonalization of some intra-block renormalized Hamiltonian.

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Improved matrix product operator renormalization group: application to the N-color random Ashkin–Teller chain

Cited by 4 publications

References 38 publications

Tensor network renormalization group study of spin-1 random Heisenberg chains

Tensor network renormalization group study of spin-1 random Heisenberg chains

Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models

Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder

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