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

Yan, Zheng; Zhou, Zheng; Syljuåsen, Olav F.; Zhang, Junhao; Yuan, Tianzhong; Lou, Jie; Chen, Yan

doi:10.48550/arxiv.1911.05433

Cited by 2 publications

(2 citation statements)

References 26 publications

(37 reference statements)

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“…It would be interesting to apply this method to study the emergent U(1) symmetry in the way we have done here. The most recent work on the quantum dimer model on the square lattice supports a mixed eight-fold degenerate phase [81] with both columnar and plaquette long-range order, as had also been observed in a previous study [77]. It will be interesting to see if a longer length scale ξ can be uniquely identified in this case, or if the splitting of the four peaks in the distribution of the angular order parameter actually corresponds to two cross-over length scales.…”

Section: Discussionsupporting

confidence: 63%

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Patil,

Shao,

Sandvik

2020

Preprint

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We consider two-dimensional q-state quantum clock models with quantum fluctuations connecting states with all-to-all clock transitions with different choices for the matrix elements. We study the quantum phase transitions in these models using quantum Monte Carlo simulations and finite-size scaling, with the aim of characterizing the cross-over from emergent U(1) symmetry at the transition (for q ≥ 4) to Zq symmetry of the ordered state. We also study classical three-dimensional clock models with spatial anisotropy corresponding to the space-time anisotropy of the quantum systems. The U(1) to Zq symmetry cross-over in all these systems is governed by a so-called dangerously irrelevant operator. We specifically study q = 5 and q = 6 models with different forms of the quantum fluctuations and different anisotropies in the classical models. In all cases, we find the expected classical XY critical exponents and scaling dimensions yq of the clock fields. However, the initial weak violation of the U(1) symmetry in the ordered phase, characterized by a Zq symmetric order parameter φq, scales in an unexpected way. As a function of the system size (length) L, close to the critical temperature φq ∝ L p , where the known value of the exponent is p = 2 in the classical isotropic clock model. In contrast, for strongly anisotropic classical models and the quantum models we find p = 3. For weakly anisotropic classical models we observe a cross-over from p = 2 to p = 3 scaling. The exponent p directly impacts the exponent ν governing the divergence of the U(1) to Zq cross-over length scale ξ in the thermodynamic limit, according to the relationship ν = ν(1 + |yq|/p), where ν is the conventional correlation length exponent. We present a phenomenological argument for p = 3 based on an anomalous renormalization of the clock field in the presence of anisotropy, possibly as a consequence of topological (vortex) line defects. Thus, our study points to an intriguing interplay between conventional and dangerously irrelevant perturbations, which may affect also other quantum systems with emergent symmetries.

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Section: Discussionsupporting

confidence: 63%

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Patil,

Shao,

Sandvik

2020

Preprint

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“…However, the numerical calculation of the constrained models is difficult which directly delays our research and understanding for these many-body systems. Quantum dimer models (QDMs) featured by strong geometric restrictions are effective low energy descriptions of many quantum spin systems [1][2][3][4][5][6]. The QDM Hamiltonian on square lattice can be written as…”

Section: Introductionmentioning

confidence: 99%

Global scheme of sweeping cluster algorithm to sample among topological sectors

Yan

2020

Preprint

Self Cite

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Quantum dimer models (QDMs) featured by strong geometric constraint are effective low energy descriptions of many quantum spin systems. The geometric restriction described by local gauge field, hinders the application of numerical algorithms. Before sweeping cluster method was applied in world-line quantum Monte Carlo (QMC) algorithm, there is only projector QMC which obey the constraints and could be used for calculation on QDMs. However, the projector QMC for QDMs has some drawbacks, e.g., it is not effective when the parameter interval away from Rokhsar-Kivelson (RK) point. That's because the projector method still lacks a cluster update to improve its efficiency. Although sweeping cluster algorithm improves the update for these systems, it also only works in one winding (topological) sector. In this paper, we improve the sweeping cluster method to sample in different winding sectors.

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

Cited by 2 publications

References 26 publications

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Global scheme of sweeping cluster algorithm to sample among topological sectors

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