Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions

Yan, Zheng; Wu, Yun; Liu, Chenrong; Syljuåsen, Olav F.; Lou, Jie; Chen, Yan

doi:10.1103/physrevb.99.165135

Cited by 50 publications

(31 citation statements)

References 37 publications

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“…The distinction between first order transition and RK-type transition is that at the first order transition point, the Z 6 angular dependence pertains, whereas at the RK point, the angular dependence of the Z 6 peaks gradually fade away, and a 𝑈 (1) symmetry emerges, characterised by a ring in the histogram (Fig. S6b) [41]. This can be seen clearly numerically that when we go along the transition line from the first order end to the RK point, the Z 6 feature gradually disappears and the six peaks connect into one ring, and after crossing the RK point, the 𝑈 (1) symmetry is broken (Fig.…”

Section: Histogram Of the Clock Order Parameter Across Rk-qcpmentioning

confidence: 99%

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Emergent Rokhsar-Kivelson point in realistic quantum Ising models

Zhou¹,

Yan²,

Liu³

et al. 2021

Preprint

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We show that the Rokhsar-Kivelson (RK) point in quantum dimer models (QDM) can emerge in realistic quantum Ising spin systems. Specifically, we investigate the 𝐽 1 -𝐽 2 -𝐽 3 transverse field Ising model on the triangular lattice with large-scale quantum Monte Carlo simulations. We find that the multicritical point in the phase diagram corresponds to the RK point of the QDM on the honeycomb lattice. We further measure the spectral functions and identify three branches of quadratic dispersions. In the phase diagram, we also find a sequence of incommensurate states, which meet the microscopic ingredients for the 'Cantor deconfinement' scenario. Our study provides a promising direction to realise the RK deconfinement in experimental platforms such as magnetic materials or programmable Rydberg arrays.

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Section: Histogram Of the Clock Order Parameter Across Rk-qcpmentioning

confidence: 99%

“…( 1). This term counts the overall number of flippable plaquettes, which involves unrealistic multiple spin interactions [27,41,42] in the spin representation. Therefore it is greatly appreciated to substitute the 𝑣 term with pairwise spin interactions realistic in nature.…”

mentioning

confidence: 99%

Emergent Rokhsar-Kivelson point in realistic quantum Ising models

Zhou¹,

Yan²,

Liu³

et al. 2021

Preprint

Self Cite

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“…By choosing clusters to update based on the flippable plaquettes in the expected ground state, we increase the likelihood of having segments with classically flippable clusters, and thus p α = 1. We have yet to investigate applying other cluster based update moves to the cluster selection stage, though some candidates exist such as the sweeping cluster update 34 .…”

Section: A Semiclassical Rvb Updatementioning

confidence: 99%

Quantum orders in the frustrated Ising model on the bathroom tile lattice

Hearth,

Morampudi,

Laumann

2022

Preprint

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We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. The phase diagram exhibits a wealth of 2+1d physics, including 1. classical Coulomb dimer liquids of both square and triangular lattice types; 2. quantum order-by-disorder induced phases breaking Z4, Z6, and Z8 symmetries; 3. finite temperature Kosterlitz-Thouless (KT) phases floating over the Z6 and Z8 orders; and, 4. staircases of (in)commensurate symmetry breaking phases at intermediate coupling. We establish this elaborate phase diagram using a combination of dimer model mapping, perturbation theory, Landau analysis and Stochastic Series Expansion Quantum Monte Carlo (QMC-SSE). Our results provide a baseline for studying frustrated magnetism with D-Wave architecture annealers, where the 4-8 lattice can be embedded naturally without 'cloning', reducing the number of competing energy scales. Simulations with the D-Wave 2000Q demonstrate qualitative agreement with the high temperature portion of the phase diagram, but are unable to access the low temperature phases.

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“…As shown in Fig. 3(b), the constraint (triangle rule) will restrict the Hilbert space so that the TFIM is equivalent to a dual honeycomb lattice dimer model [47][48][49][50][51][52] by mapping two parallel spins to one dimer on the dual lattice. Then, the triangle rule is translated to dimer counterpart that each dual site belongs to one and only one dimer.…”

Section: Sqa and Topologymentioning

confidence: 99%

Sweeping quantum annealing algorithm for constrained optimization problems

Yan¹,

Zhou²,

Wang³

et al. 2021

Preprint

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As a typical quantum computing algorithm, quantum annealing is widely used in the optimization of glass-like problems to find the best solution. However, the optimization problems in constrained complex systems usually involve topological structures, and the performance of the quantum annealing algorithm is still largely unknown. Here, we take an Ising system as a typical example with local constraints accompanied by intrinsic topological properties that can be implemented on quantum computing platforms such as the D-wave machine, and study the effectiveness of the quantum annealing algorithm in its optimization and compare it with that of the thermal annealing. We find that although conventional quantum annealing is difficult for the optimization of constrained topological problems, a generalized algorithm --- the sweeping quantum annealing method --- can be designed and solve the problem with better efficiency than both conventional quantum and thermal annealing algorithms. The sweeping quantum annealing algorithm, therefore, opens up a promising avenue for quantum computing of constrained problems and can be readily employed on the optimizations in quantum material design, engineering, and even social sciences.

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Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions

Cited by 50 publications

References 37 publications

Emergent Rokhsar-Kivelson point in realistic quantum Ising models

Emergent Rokhsar-Kivelson point in realistic quantum Ising models

Quantum orders in the frustrated Ising model on the bathroom tile lattice

Sweeping quantum annealing algorithm for constrained optimization problems

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