Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

Banerjee, Debasish; Bögli, Michael; Hofmann, Christoph P.; Jiang, Fu-Jiun; Widmer, Philippe; Wiese, U.‐J.

doi:10.1103/physrevb.94.115120

Cited by 22 publications

(21 citation statements)

References 48 publications

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“…Phase diagram.-Our second question is where is the boundary of the mixed state, i. e., what is the entire phase diagram? Based on field theory analysis combined with exact diagonalization method, recent studies have shown that there should be no phase transition points from the classical limit (V = −∞) to the RK point [14,15]. A similar trend can also be seen in Fig.…”

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confidence: 70%

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Widely existing mixed phase structure of quantum dimer model on square lattice

Yan,

Zhou,

Syljuåsen

et al. 2019

Preprint

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Constraint is an important property in low-energy physics, but it also bring a lot of difficulties for numeric calculation. The quantum dimer model is a low-energy description of many spin models, but its phase diagram is still controversial, even on the square lattice. In this article, we focus on the square lattice quantum dimer model and give a unified conclusion about its phase diagram which reconciles conflicting results given in the literature. With our newly developed sweeping cluster method, we studied the phase diagram of the almost full parameter space by introducing the definition of pair correlation function and other supporting evidence to distinguish the mixed phase from the columnar phase with high precision. In particular, we find that the ground state corresponds to the mixed phase for a vast parameter region.

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confidence: 70%

“…1, where the ground state becomes the staggered state. The same phase diagram is also supported by Metropolis Monte Carlo simulations on height model equivalents of the square lattice QDM [14,15] and the frustrated transverse field Ising model which is equal to a parameter point (V = 0) of QDM [18].…”

mentioning

confidence: 54%

Widely existing mixed phase structure of quantum dimer model on square lattice

Yan,

Zhou,

Syljuåsen

et al. 2019

Preprint

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“…The signs and magnitudes of the vector fields E are assigned based on the rule described in Fig. 3d 15,30 . Its line integral, ∫ ⋅ γ E l d along a directed line γ crossing the edges, is the sum of the vector along the line with its sign taken along the line's direction.…”

Section: Studies Of the Moments During A Slow Cooldown On Another Sammentioning

confidence: 99%

Classical topological order in the kinetics of artificial spin ice

et al. 2018

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Systems of interacting nanomagnets known as artificial spin ice 1-4 have allowed the design, realization and study of geometrically frustrated exotic collective states 5-10 that are absent in natural magnets. We have experimentally measured 11,12 the thermally induced moment fluctuations in the Shakti geometry of artificial spin ice. We show that its disordered moment configuration is a topological phase described by an emergent dimer-cover model 13 with excitations that can be characterized as topologically charged defects. Examination of the lowenergy dynamics of the system confirms that these effective topological charges have long lifetimes associated with their topological protection, that is, they can be created and annihilated only as charge pairs with opposite sign and are kinetically constrained. This manifestation of classical topological order 14-19 demonstrates that geometrical design in nanomagnetic systems can lead to emergent, topologically protected kinetics that can limit pathways to equilibration and ergodicity. Artificial spin ices are lithographically fabricated systems of interacting single-domain nanomagnets. These systems can be used to investigate the collective magnetic behaviour of interacting moments as effective models for understanding the complex phenomena of frustration. Each nanomagnet moment aligns along the edges of a lattice and points towards or away from the lattice vertices. In their low-energy collective states, the moments enter a so-called ice-manifold; an ensemble in which, at each vertex, the difference between the number of moments pointing in and out is minimized, leading to the ice-rule (2-in/2-out 20 at vertices where four moments meet or 1-in/2-out, 2-in/1-out at vertices where three moments meet). Originally inspired by rare-earth pyrochlore spin ice materials, these artificial spin ice systems evolved towards new geometries 5,6 , with exotic phases absent in natural magnets 2,3,7,8,21. Recent experimental works have characterized the thermal fluctuations of the individual magnetic moments, opening new vistas in the real-time, real-space analysis of frustration 11,12,22-25. The Shakti lattice geometry 5-7 (Fig. 1) is a decimation of the square ice lattice geometry. In Fig. 1e, we show the possible moment configurations at vertices and label them by the number of islands at each vertex (the coordination number, z) and by their relative energy hierarchy. The collective ground state is a configuration in which the z = 2 and z = 4 vertices are all in their lowest energy state (that is, type I 4 for the four-island vertices and type I 2 for the twoisland vertices) while only half of the z = 3 vertices lie in their lowest

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“…Due to the absence of the reference configuration in the chosen basis of the quantum height model, the clusters grow quite large to occupy about 80 − 90% of the space-time volume, which makes the cluster algorithm not much better than a local update Metropolis algorithm. However, a combination of both these algorithms was used to study the physics of the QDM [53,54] and reliably extract the phase diagram at zero temperature. For the QDM certain other computational methods have been reported [55,56], including certain novel effective theory approaches [57].…”

Section: Pure Gauge Theoriesmentioning

confidence: 99%

Recent progress on cluster and meron algorithms for strongly correlated systems

Banerjee

2021

Preprint

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Ab-initio studies of strongly interacting bosonic and fermionic systems is greatly facilitated by efficient Monte Carlo algorithms. This article emphasizes this requirement, and outlines the ideas behind the construction of the cluster algorithms and illustrates them via specific examples. Numerical studies of fermionic systems at finite densities and at real-times are sometimes hindered by the infamous sign problem, which is also discussed. The construction of meron cluster algorithms, which can solve certain sign problems are discussed. Cluster algorithms which can simulate certain pure Abelian gauge theories (realized as quantum link models) are also discussed.

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Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

Cited by 22 publications

References 48 publications

Widely existing mixed phase structure of quantum dimer model on square lattice

Widely existing mixed phase structure of quantum dimer model on square lattice

Classical topological order in the kinetics of artificial spin ice

Recent progress on cluster and meron algorithms for strongly correlated systems

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