Quantum dynamics of the square-lattice Heisenberg model

Verresen, Ruben; Pollmann, Frank; Moessner, Roderich

doi:10.1103/physrevb.98.155102

Cited by 45 publications

(40 citation statements)

References 59 publications

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“…Regarding the nature of the excitations around (π, 0), which we discuss in (Sec. III B 3), several theories have been proposed, such as an interaction between the magnon and a double spinon mode [29,30,32] or a repulsion from continua of multimagnon (bound) states [23]. We indeed observe a dip in the magnon energy, increasing with bond dimension, in agreement with earlier iPEPS results [9].…”

Section: Dispersionsupporting

confidence: 91%

“…A recent study [23], which used time evolution of semiinfinite cylindrical systems to obtain the dynamical structure factor, proposed a simple description of the excitation nature at the M point; by moving away from the isotropic point of the Hamiltonian, i.e., λ < 1 in (20), where the case λ = 0 corresponds to the Ising limit. It was observed that for small λ three distinct types of resonances in the transverse structure factor could be identified: an isolated single magnon branch, three-magnon bound states, and combinations of a magnon and a two-magnon bound state.…”

Section: Nature Of Excitations At (π 0)mentioning

confidence: 99%

“…It has been successfully applied in many contexts, such as magnons in spin chains, spin and charge excitations in the Hubbard model and even scattering states and topologically nontrivial excitations [12,13]. An alternative technique to gain insight into the low-lying excitations with MPS is to compute dynamical structure factors, which has been used both in one dimensional systems [14][15][16][17][18][19][20] as well on two-dimensional semi-infinite cylinders [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…Since iPEPS cannot be contracted exactly and approximate contraction schemes are needed, the summation over real space perturbations constitutes significant challenges. First applied in frustration-free Hamiltonian models [8], yielding an accurate value of the gap in the Affleck-Kennedy-Lieb-Tasaki model, the iPEPS excitation ansatz has recently correctly reproduced the behavior of the spin-1 /2 Heisenberg antiferromagnet [9], where the energy deviates from conventional linear spin wave theory and the underlying physics is still debated [23,[29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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Excitations with projected entangled pair states using the corner transfer matrix method

Ponsioen¹,

Corboz²

2020

Phys. Rev. B

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We present an extension of a framework for simulating single quasiparticle or collective excitations on top of strongly correlated quantum many-body ground states using infinite projected entangled pair states, a tensor network ansatz for two-dimensional wave functions in the thermodynamic limit. Our approach performs a systematic summation of locally perturbed states in order to obtain excited eigenstates localized in momentum space, using the corner transfer matrix method, and generalizes the framework to arbitrary unit cell sizes, the implementation of global Abelian symmetries and fermionic systems. Results for several test cases are presented, including the transverse Ising model, the spin-1 /2 Heisenberg model, and a free fermionic model, to demonstrate the capability of the method to accurately capture dispersions. We also provide insight into the nature of excitations at the k = (π, 0) point of the Heisenberg model.

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Section: Dispersionsupporting

confidence: 91%

Section: Nature Of Excitations At (π 0)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Excitations with projected entangled pair states using the corner transfer matrix method

Ponsioen¹,

Corboz²

2020

Phys. Rev. B

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“…One of the key features that allows us to perform machine learning of the regular-to-chaos transition is the difference in statistical properties of |ψ n | 2 in the two regimes. While in the chaotic case the wavefunctions have Gaussian statistics, in regular case the probability distribution is non-universal and has a power-law singularity at small values of ψ n [36].…”

mentioning

confidence: 99%

Revealing quantum chaos with machine learning

et al. 2020

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Understanding the properties of quantum matter is an outstanding challenge in science. In this work, we demonstrate how machine learning methods can be successfully applied for the classification of various regimes in single-particle and many-body systems. We realize neural network algorithms that perform a classification between regular and chaotic behavior in quantum billiard models with remarkably high accuracy. By taking this method further, we show that machine learning techniques allow to pin down the transition from integrability to many-body quantum chaos in Heisenberg XXZ spin chains. Our results pave the way for exploring the power of machine learning tools for revealing exotic phenomena in complex quantum many-body systems.Introduction. Significant attention to machine learning techniques is related to their applications in tasks of finding patterns in data, such as image recognition, speech analysis, computer vision, and many other domains [1]. Quantum physics is well known to produce atypical patterns in data, which are in principle can be revealed using machine learning methods [2]. This idea has stimulated an intensive ongoing research of this subject. The scope so far includes identification of phases of quantum matter and detecting phase transitions [4][5][6][7][8][9][10][11], as well as representing quantum states of many-body systems in regimes that are intractable for existing exact numerical approaches [15][16][17]. Another branch of research is related to the applications of machine learning tools to the analysis of experimental data [18][19][20]. Recently, a machine learning approach has been used for processing data from gas microscopes and evaluating predictions of competing theories that describe the doped Hubbard model without a bias towards one of the theories [21].Remarkable progress on building large-scale quantum simulators has opened fascinating prospects for the observation of novel quantum phases and exotic states [22][23][24][25]. They also provide interesting insights to traditionally challenging problems in studies of complex quantum systems, such as investigation of quantum critical dynamics and quantum chaos [26]. Quantum systems with chaotic behaviour are of great interest in the view of a possibility to explore quantum scars in them [27]. Quantum many-body scars can be potentially compatible with long-lived states, which are of importance for quantum information processing. A standard criterion for the separation between regular and chaotic regimes is based on the nearest-neighbor energy level statistics [28,29]: Poisson and Wigner-Dyson distributions correspond to integrable and chaotic systems, respectively. However, the energy level statistics of highly excited states is not always directly accessible in experiments.From the machine learning perspective, an interesting problem is to understand whereas it is possible to distinguish between regular and chaotic behavior, in the best-

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Progress on stochastic analytic continuation of quantum Monte Carlo data

Shao

Sandvik

2023

Physics Reports

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Quantum dynamics of the square-lattice Heisenberg model

Cited by 45 publications

References 59 publications

Excitations with projected entangled pair states using the corner transfer matrix method

Excitations with projected entangled pair states using the corner transfer matrix method

Revealing quantum chaos with machine learning

Progress on stochastic analytic continuation of quantum Monte Carlo data

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