Columnar dimer and plaquette resonating-valence-bond orders in the quantum dimer model

Leung, Pak Wo; Chiu, King Chuen; Runge, K.

doi:10.1103/physrevb.54.12938

Cited by 78 publications

(116 citation statements)

References 13 publications

(10 reference statements)

Supporting

Mentioning

112

Contrasting

Order By: Relevance

“…As was already noted in Ref. 25, this order parameter (and associated quantities) is sensitive to translation symmetry breaking and a non-zero expectation value detects both columnar and plaquette ordering. Looking at the phase of Ψ col can in principle discriminate between the two phases: however the phase turns out to be a noisy observable in our simulations and has no practical use.…”

Section: Order Parametersmentioning

confidence: 92%

“…The resulting state breaks translation invariance but is invariant under π/2 rotation with respect to the center of any plaquette (see Ref. 25 for an illustration). In the quantum system, a plaquette phase has a (slightly) higher potential energy than a columnar crystal, but the stronger dimer resonances lower the plaquette state energy through the kinetic terms of the quantum Hamiltonian.…”

Section: Description Of Plaquette Orderingmentioning

confidence: 99%

“…The T = 0 phase diagram of the QDM is usually accepted as this [25,44,45] (with the standard notation of t for the kinetic energy gained by flipping a plaquette): for large negative v/t, the system is in a columnar phase. Increasing v/t, the QDM experiences a quantum phase transition to a plaquette phase at a quite uncertain value of v/t (see discussion below).…”

Section: A Connection To Other Classical Modelsmentioning

confidence: 99%

“…This also holds in a plaquette phase, but is no longer true for a columnar state. A convenient way of monitoring the π/2-rotation symmetry [25] is the Dimer Symmetry Breaking:…”

Section: Order Parametersmentioning

confidence: 99%

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Classical dimers with aligning interactions on the square lattice

et al. 2006

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We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the non-interacting case of dimer coverings, including a Bethe Ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model and a free field analysis of height fluctuations.

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Section: Order Parametersmentioning

confidence: 92%

Section: Description Of Plaquette Orderingmentioning

confidence: 99%

Section: A Connection To Other Classical Modelsmentioning

confidence: 99%

“…This also holds in a plaquette phase, but is no longer true for a columnar state. A convenient way of monitoring the π/2-rotation symmetry [25] is the Dimer Symmetry Breaking:…”

Section: Order Parametersmentioning

confidence: 99%

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Classical dimers with aligning interactions on the square lattice

et al. 2006

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“…We have not studied this problem numerically ourselves but we refer the reader to the literature on the ferromagnetically stacked magnet 39,48 and the quantum dimer model. 49,50 …”

Section: Villain's Odd Model: the Fully Frustrated Square Latticementioning

confidence: 99%

Ising models of quantum frustration

2001

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We report on a systematic study of two dimensional, periodic, frustrated Ising models with a quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagome lattice antiferromagnets, fully frustrated models on the square and hexagonal (honeycomb) lattices, a planar analog of the pyrochlore antiferromagnet, a pentagonal lattice antiferromagnet as well as a two quasi one-dimensional lattices that have considerable pedagogical value. All of these exhibit a macroscopic degeneracy at T = 0 in the absence of the transverse field, which enters as a singular perturbation. We analyze these systems with a combination of a variational method at weak fields, a perturbative Landau-Ginzburg-Wilson (LGW) approach from large fields as well as quantum Monte Carlo simulations utilizing a cluster algorithm. Our results include instances of quantum order arising from classical criticality (triangular lattice) or classical disorder (pentagonal and probably hexagonal) as well as notable instances of quantum disorder arising from classical disorder (kagome). We also discuss the effect of a finite temperature, as well as the interplay between longitudinal and transverse fields-in the kagome problem the latter gives rise to a non-trivial phase diagram with bond-ordered and bond-critical phases in addition to the disordered phase. We also note connections to quantum dimer models and thereby to the physics of Heisenberg antiferromagnets in short-ranged resonating valence bond phases that have been invoked in discussions of high-temperature superconductivity.

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Frustrated Quantum Magnets

Lhuillier

Misguich

2002

High Magnetic Fields

140

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A description of different phases of two dimensional magnetic insulators is given.The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Néel phases. Order by disorder selection is illustrated. All these phases break SU (2) symmetry and are gapless phases with ∆S z = 1 magnon excitations.Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful ∆S = 0, or1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.

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Columnar dimer and plaquette resonating-valence-bond orders in the quantum dimer model

Cited by 78 publications

References 13 publications

Classical dimers with aligning interactions on the square lattice

Classical dimers with aligning interactions on the square lattice

Ising models of quantum frustration

Frustrated Quantum Magnets

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