Worm-algorithm-type simulation of the quantum transverse-field Ising model

Huang, Chun-Jiong; Liu, Longxiang; Jiang, Y.; Deng, Youjin

doi:10.1103/physrevb.102.094101

Cited by 14 publications

(12 citation statements)

References 61 publications

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“…In this way, a different choice of q and g generates a separate set of {G(iω n ), A(Ω)}, which contributes one sample to the training dataset. For the testing dataset, the imaginary-time Green's function G(iω n ) is computed using a Worm-type quantum Monte Carlo method (see Appendix B for details) [23], where noise with unknown strength is intrinsically embedded. As labels, their corresponding A(Ω) are still obtained by the exact mapping to free fermions under the same parameters q and g. Fig.…”

Section: B the Transverse Field Ising Modelmentioning

confidence: 99%

“…We closely follow Ref. [23] to map spin operators into hard-core boson operators such that the resulting partition function can be efficiently sampled by the Worm algorithm [25,26]. We first perform a spin rotation around the y-axis for 90 degrees and the spin rotational operators πl is defined as…”

Section: Appendix A: Exact Solution For the Transverse Ising Modelmentioning

confidence: 99%

“…(B6), the weight of the configuration is positive and can be sampled by the Monte Carlo method. Following the detailed update procedures in [23], the partition function can be efficiently sampled by Worm-type algorithms. The imaginary-time Green's function G(l − l , τ ) defined in Eq.…”

Section: Appendix A: Exact Solution For the Transverse Ising Modelmentioning

confidence: 99%

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Noise Enhanced Neural Networks for Analytic Continuation

Yao,

Wang,

Yao

et al. 2021

Preprint

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Analytic continuation maps imaginary-time Green's functions obtained by various theoretical/numerical methods to real-time response functions that can be directly compared with experiments. Analytic continuation is an important bridge between many-body theories and experiments but is also a challenging problem because such mappings are ill-conditioned. In this work, we develop a neural network-based method for this problem. The training data is generated either using synthetic Gaussian-type spectral functions or from exactly solvable models where the analytic continuation can be obtained analytically. Then, we applied the trained neural network to the testing data, either with synthetic noise or intrinsic noise in Monte Carlo simulations. We conclude that the best performance is always achieved when a proper amount of noise is added to the training data. Moreover, our method can successfully capture multi-peak structure in the resulting response function for the cases with the best performance. The method can be combined with Monte Carlo simulations to compare with experiments on real-time dynamics.

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Section: B the Transverse Field Ising Modelmentioning

confidence: 99%

Section: Appendix A: Exact Solution For the Transverse Ising Modelmentioning

confidence: 99%

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Noise Enhanced Neural Networks for Analytic Continuation

Yao,

Wang,

Yao

et al. 2021

Preprint

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“…For the purely transverse field Ising model on a square lattice (Eq. 9), existing variational and cluster Monte-Carlo calculations [64][65][66][67] shows the strength of the transverse field ≈ 3J is the critical point for the phase transition between the symmetry broken τ z magnetically ordered state, i.e. τ z i = 0 and the paramagnet state, i.e.…”

Section: A Toric Code Limitmentioning

confidence: 99%

“…In continuation with our soft mode treatment, we now implement the integer constraint on A āb softly through the potential −w cos(2πA) (w > 0) (67) such that the whole action (Eq. 55) becomes…”

Section: The Mutual Z2 Gauge Theorymentioning

confidence: 99%

Phases and quantum phase transitions in an anisotropic ferromagnetic Kitaev-Heisenberg- Γ magnet

2020

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Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

Dai¹,

Li²,

Chen³

2022

Chinese Phys. B

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We investigate quantum phase transitions for q = 2-, 3-, and 4-state quantum Potts models on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen-Shannon divergence, the relative entropy of coherence, and the l 1 norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.

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Worm-algorithm-type simulation of the quantum transverse-field Ising model

Cited by 14 publications

References 61 publications

Noise Enhanced Neural Networks for Analytic Continuation

Noise Enhanced Neural Networks for Analytic Continuation

Phases and quantum phase transitions in an anisotropic ferromagnetic Kitaev-Heisenberg- Γ magnet

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

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