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arXiv:1501.02242 · Physical review. B./Physical review. B

Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps

Thiago Milanetto Schlittler, Rémy Mosseri, Thomas Barthel

Published Nov 21, 2017• 16 citations
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Abstract

The phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice is computed numerically, extending on earlier work by Moessner, Sondhi, and Chandra. The different ground state phases are studied in detail using several local and global observables. In addition, we analyze imaginary-time correlation functions to determine ground state energies as well as gaps to the first excited states. This leads in particular to a confirmation that the intermediary so-called plaquette phase is gapped. On the technical side, we describe an efficient world-line quantum Monte Carlo algorithm with improved cluster updates that increase acceptance probabilities by taking account of potential terms of the Hamiltonian during the cluster construction. The Monte Carlo simulations are supplemented with variational computations.

DOI
10.1103/physrevb.96.195142

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The phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice is computed numerically, extending on earlier work by Moessner, Sondhi, and Chandra. The different ground state phases are studied in detail using several local and global observables. In addition, we analyze imaginary-time correlation functions to determine ground state energies as well as gaps to the first excited states. This leads in particular to a confirmation that the intermediary so-called plaquette phase is gapped. On the technical side, we describe an efficient world-line quantum Monte Carlo algorithm with improved cluster updates that increase acceptance probabilities by taking account of potential terms of the Hamiltonian during the cluster construction. The Monte Carlo simulations are supplemented with variational computations.
We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations, supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the "devil's staircase" scenario [Eduardo Fradkin et al. Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.
Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al., Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory suggested a dimerized, color-ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension DDD. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small DDD the dimer state has a lower variational energy than the plaquette state; however, for large DDD it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are nonchiral flux states.
Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. 86, 1881 (2001)].
The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
The quantum dimer and loop models attract great attention, partially because the fundamental importance in the phases and phase transitions emerging in these prototypical constrained systems, and partially due to their intimate relevance toward the on-going experiments on Rydberg atom arrays in which the blockade mechanism naturally enforces the local constraint. Here we show, by means of the sweeping cluster quantum Monte Carlo method, the complete ground state phase diagram of the fully packed quantum loop model on the square lattice. We find between the lattice nematic (LN) phase with strong dimer attraction and the staggered phase (SP) with strong dimer repulsion, there emerges a resonating plaquette (RP) phase with off-diagonal translational symmetry breaking. Such a quantum phase is separated from the LN via a first order transition and from the SP by the famous Rokhsar-Kivelson point. Our renormalization group analysis reveals the different flow directions, fully consistent with the order parameter histogram in Monte Carlo simulations. The realization and implication of our phase diagram in Rydberg experiments are proposed.
The quantum dimer model is a low-energy effective model for many magnetic systems (materials) that are candidates for quantum spin liquids. It has strict local constraints which is described by gauge field theory. However, since constraints hinder the application of numerical algorithms, the phase diagrams of quantum dimer models are still controversial, even on a square lattice. The core controversy is whether the mixed state exists due to the restriction. In this paper, we give strong evidence to solve this dispute. With our sweeping cluster quantum Monte Carlo method, we studied the phase diagram of a large parameter region by introducing the definition of the 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 belongs to the mixed phase for a vast parameter region.