Path-integral Monte Carlo method for the local<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>Berry phase

Motoyama, Yuichi; Todo, Synge

doi:10.1103/physreve.87.021301

Cited by 16 publications

(24 citation statements)

References 27 publications

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“…where (Σ) ij ≡ k C (i, j) and the composite kernel k C (i, j) is defined by Eq. (14). The inferred parameter is q = (T c , c 1 , c 2 , c 3 , θ 2 , θ 0,0 , θ 0,1 , · · · , θ M,0 , θ M,1 ) t .…”

Section: Practical Procedures Of the Kernel Methodsmentioning

confidence: 99%

Kernel method for corrections to scaling

Harada

2015

Phys. Rev. E

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Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.

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Section: Practical Procedures Of the Kernel Methodsmentioning

confidence: 99%

Kernel method for corrections to scaling

Harada

2015

Phys. Rev. E

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“…I demonstrate a QMC method to solve for the Berry curvature with respect to global (as opposed to local [53]) coupling parameters. Having seen that this idea works for a simple case, it is readily extensible to other models.…”

Section: Discussionmentioning

confidence: 99%

Measuring Berry curvature with quantum Monte Carlo

Kolodrubetz

2014

Phys. Rev. B

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The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well-studied in the regimes of few-body physics and non-interacting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve it. In this paper we fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. We demonstrate our algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is non-integrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, we show that our algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians. Our algorithm scales similarly to conventional methods as a function of system size and energy gap, and therefore should prove a valuable tool in investigating the quantum geometry of many-body systems.Comment: 4 pages + 2 page appendix, 2 figure

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“…For updating the worldline configuration, we employ the loop cluster algorithm [28][29][30]. In the loop cluster algorithm, one can represent the Berry connection as a function of loop configuration (improved estimator) instead of the worldline configuration [23]. It should be noted that in the present projector Monte Carlo, the states at τ = 0 and β are fixed to some reference state, |φ , which break edge loops and prevent these from flipping.…”

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confidence: 99%

“…where the loop indices and run over all closed loops. For N = 2, this estimator is reduced to the one derived in the past work [23]. A typical loop configuration for the SU(N ) AFH model is shown in the right panel of Fig.…”

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confidence: 99%

ZN Berry phase and symmetry-protected topological phases of the SU( N ) antiferromagnetic Heisenberg chain

Motoyama

Todo

2018

Phys. Rev. B

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The local ZN quantized Berry phase for the SU(N ) antiferromagnetic Heisenberg spin model is formulated. This quantity, which is a generalization of the local Z2 Berry phase for SU(2) symmetry, has a direct correspondence to the number of singlet pairs spanning on a particular bond, and is effective as a tool to characterize and classify the various symmetry protected topological phases of one-dimensional SU(N ) spin systems. We extend the path-integral quantum Monte Carlo method for the Z2 Berry phase in order to calculate the ZN Berry phase numerically. We demonstrate our method by calculating the Z4 Berry phase for the bond-alternating SU(4) antiferromagnetic Heisenberg chain, which is represented by the Young diagram of four columns.

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Path-integral Monte Carlo method for the localZ2Berry phase

Cited by 16 publications

References 27 publications

Kernel method for corrections to scaling

Kernel method for corrections to scaling

Measuring Berry curvature with quantum Monte Carlo

ZN Berry phase and symmetry-protected topological phases of the SU( N ) antiferromagnetic Heisenberg chain

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