Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions

Jian, Chao-Ming; Zaletel, Michael P.

doi:10.1103/physrevb.93.035114

Cited by 25 publications

(46 citation statements)

References 39 publications

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“…One such construction was given recently with S = 1 model on a square lattice [5], while attempts to construct featureless states for S = 1/2 spins on a honeycomb lattice has met with partial success so far [5][6][7]. In this paper, we provide an explicit construction of the spin-1/2 wave function on a honeycomb lattice that preserves the full set of lattice symmetries plus timereversal and SU(2) spin rotation, in addition to being devoid of topological order.…”

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confidence: 99%

Featureless quantum insulator on the honeycomb lattice

et al. 2016

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We show how to construct fully symmetric, gapped states without topological order on a honeycomb lattice for S = 1/2 spins using the language of projected entangled pair states (PEPS). An explicit example is given for the virtual bond dimension D = 4. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking, and the existence of energy gap in the proposed wave functions, are checked by numerical calculations of the entanglement entropy and various correlation functions. Our work provides the first explicit realization of a featureless quantum insulator for spin-1/2 particles on a honeycomb lattice.Introduction -A modern theme of much interest in condensed matter systems is the classification of possible phases of quantum matter in low dimensions. First noted in the context of quantum Hall physics, it has become clear that different quantum phases are labeled often by their topological characters rather than broken symmetries as in the conventional Ginzburg-Landau paradigm [1]. How to define such quantum orders and classify states accordingly in a precise way has intrigued theorists for several decades.

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Featureless quantum insulator on the honeycomb lattice

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“…Such featureless paramagnetic states [4] as gapped QSL states, which are both fully symmetric and unfractionalized, are particularly interesting, since their existence for some specific broad classes of models is often strictly forbidden. An example of such a constraint is the Lieb-Schultz-Mattis theorem [5] for d = 1 chains and its extensions to systems with d > 1 [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…There are also, however, various field-theoretical arguments that tend to disfavor their existence (see, e.g., Refs. [4,8,9]). For both these reasons, it is of great interest to examine models where they are not specifically excluded by any existing theorems and, possibly, also for which idealized, candidate wave functions can be constructed [4].…”

Section: Introductionmentioning

confidence: 99%

Ground-state phases of the spin-1J1−J2Heisenberg antiferromagnet on the honeycomb lattice

Bishop²

2016

Phys. Rev. B

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We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling J 1 > 0 and frustrating next-nearest-neighbor coupling J 2 ≡ κJ 1 > 0, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range 0 < κ < 1 we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice Néel order for κ < κ c 1 = 0.250 (5) (5) we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range κ i c < κ < κ c 2 we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

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“…The existence of such a featureless state is consistent with the Lieb-Schultz-Mattis theorem [24] in two dimensions [25][26][27][28][29][30]. Although its wave function has been microscopically constructed [31][32][33][34], the corresponding parent Hamiltonian is still unclear. Hence, it would be helpful to understand the physical mechanism for the featureless state in order to get its Hamiltonian.…”

Section: Introductionmentioning

confidence: 71%

“…Also we do not know whether the featureless paramagnet from our approach is the same phase as the one constructed in Refs. [31,33,34], which is a crystalline symmetry-protected topological phase [32].…”

Section: Summary and Discussionmentioning

confidence: 99%

Possible phases of the spin- 12 XXZ model on a honeycomb lattice by boson-vortex duality

2018

Phys. Rev. B

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Motivated by recent numerical work, we use the boson-vortex duality to study the possible phases of the frustrated spin-1 2 J1 − J2 XXZ models on the honeycomb lattice. By condensing the vortices, we obtain various gapped phases that either break certain lattice symmetry or preserve all the symmetries. The gapped phases breaking lattice symmetries occur when the vortex band structure has two minima. Condensing one of the two vortex flavors leads to an Ising ordered phase, while condensing both vortex flavors gives rise to a valence-bond-solid state. Both of those phases have been observed in the numerical studies of the J1 − J2 XXZ honeycomb model. Furthermore, by tuning the band structure of vortex and condensing it at the Γ point, we obtain a featureless paramagnet. But the precise nature of this featureless state is still unclear and needs future study.

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Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions

Cited by 25 publications

References 39 publications

Featureless quantum insulator on the honeycomb lattice

Featureless quantum insulator on the honeycomb lattice

Ground-state phases of the spin-1J1−J2Heisenberg antiferromagnet on the honeycomb lattice

Possible phases of the spin- 12 XXZ model on a honeycomb lattice by boson-vortex duality

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