Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State

Schroeter, Darrell F.; Kapit, Eliot; Thomale, Ronny; Greiter, Martin

doi:10.1103/physrevlett.99.097202

Cited by 148 publications

(164 citation statements)

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“…However, the variational studies based on projected fermionic parton wave functions favor a gapless U(1) Dirac spin liquid (DSL) with competing ground-state energy [21][22][23][24]. Near the NN model, a robust chiral spin liquid (CSL) [25][26][27][28] is unambiguously established by introducing second-and third-neighbor couplings or chiral interaction [29][30][31][32][33][34][35]. This CSL spontaneously breaks time-reversal symmetry (TRS) and is identified as the ν = 1/2 bosonic fractional quantum Hall state.…”

Section: Introductionmentioning

confidence: 99%

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

Gong

Sheng

2016

Phys. Rev. B

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By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-1/2 Heisenberg model with the first-neighbor (J 1 ), second-neighbor (J 2 ), and additional scalar chiral interaction J χ S i · (S j × S k ) on the triangular lattice. In the nonmagnetic phase of the J 1 -J 2 triangular model with 0.08 J 2 /J 1 0.16, recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B 92, 041105(R) (2015) and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403(R) (2015)] find a possible gapped spin liquid with the signal of a competition between a chiral and a Z 2 spin liquid. Motivated by the DMRG results, we consider the chiral interaction J χ S i · (S j × S k ) as a perturbation for this nonmagnetic phase. We find that with growing J χ , the gapless U(1) Dirac spin liquid, which has the best variational energy for J χ = 0, exhibits the energy instability towards a gapped spin liquid with nontrivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number C = 1/2 and twofold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the nonmagnetic phase of the J 1 -J 2 triangular model.

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Section: Introductionmentioning

confidence: 99%

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

Gong

Sheng

2016

Phys. Rev. B

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“…The model further supports gapped bulk excitations described by 2π-kinks in a sine-Gordon coupling of two neighboring chains (10). Since the total spin of the system is given by…”

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confidence: 99%

“…The CSL has been an invaluable seed for new concepts such as topological order [8], providing a direct perspective on the fundamental relations between FQHE, spin liquids, and superconductivity [5,9]. Despite its high relevance as a paradigm formulated via wave functions, the first Hamiltonian for which the CSL is the (aside from topological degeneracies) unique ground state was only identified two decades after the liquid had been proposed [10]. The approach was subsequently expanded to yield different classes of such trial Hamiltonians [11], where the latest and more generic versions are more short-ranged than the initial microscopic models: they involve 2-body and 3-body spin interactions which can be deduced from the explicit construction of appropriate annihilation operators [12] or null operators in conformal field theory [13].…”

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confidence: 99%

“…While readily implemented in a language of wave functions, this method of obtaining a CSL state in two steps-writing it out in the continuum and then projecting it onto the lattice-is not available in a description in terms of Hamiltonians, such as our CWC. In all known constructions [10][11][12][13] of parent Hamiltonians of the KL state, P and T violation is implemented through a three-spin interaction of the form S i (S j × S k ), where i, j, and k are three lattice sites on a plaquette.…”

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confidence: 99%

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Coupled-wire construction of chiral spin liquids

et al. 2015

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We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap, and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level k with parafermionic edge states.PACS numbers: 71.10. Pm, 75.10.Kt, Introduction.-The experimental discovery [1] and conceptual understanding [2] of the fractional quantum Hall effect (FQHE) had a tremendous impact on contemporary research of strongly correlated electron systems. In particular, it triggered interest in topologically ordered quantum states of matter, which since then have persisted as a predominant focus. Following up on an idea by D. H. Lee, Kalmeyer and Laughlin [3,4] proposed the chiral spin liquid [5,6] (CSL) as a fractionally quantized Hall liquid for bosonic spin flip operators acting on a spin-polarized reference state. Fractionalization of charge for FQHE relates to fractionalization of spin for the CSL, which supports S = 1/2 spinons obeying halfFermi statistics [7]. The CSL has been an invaluable seed for new concepts such as topological order [8], providing a direct perspective on the fundamental relations between FQHE, spin liquids, and superconductivity [5,9]. Despite its high relevance as a paradigm formulated via wave functions, the first Hamiltonian for which the CSL is the (aside from topological degeneracies) unique ground state was only identified two decades after the liquid had been proposed [10]. The approach was subsequently expanded to yield different classes of such trial Hamiltonians [11], where the latest and more generic versions are more short-ranged than the initial microscopic models: they involve 2-body and 3-body spin interactions which can be deduced from the explicit construction of appropriate annihilation operators [12] or null operators in conformal field theory [13]. In particular, non-Abelian chiral spin liquids with level k parafermionic spin excitations have been proposed [12,14], which nurture the hope for alternative scenarios of topological quantum computation in frustrated magnets and Mott regimes of alkaline earth atoms deposited in optical lattices [15,16].Since their discovery, CSLs have been appreciated as a realisation of a bosonic Laughlin state at Landau level filling fraction ν = 1/2 on a spin lattice. Naturally, the CSL of Refs. 3 and 4 can be defined on any lattice [17,18], which becomes mathematically transparent via the generalized Perelomov identity [19] for lattices with a primitive unit cell. Some of these motifs have later reappeared in the field of fractional Chern insulators [20][21][22]. As

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“…[45][46][47] CSLs have also been found in a variety of other exactly solvable models. [48][49][50][51][52][53][54] The CSL is, however, intrinsically a two-dimensional phenomenon, so it is natural to ask about non-magnetic ground states of SU (N ) antiferromagnetic Heisenberg models in three dimensions. In this paper, we address this question by a large-N study of a class of SU (N ) Heisenberg models on the simple cubic lattice, and find a rich phase diagram as a function of k including cluster states, but also more intricate inhomogenous states.…”

Section: Introductionmentioning

confidence: 99%

Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions

Song

Hermele

2013

Phys. Rev. B

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We study a class of SU (N ) Heisenberg models, describing Mott insulators of fermionic ultra-cold alkaline earth atoms on the three-dimensional simple cubic lattice. Based on an earlier semiclassical analysis, magnetic order is unlikely, and we focus instead on a solvable large-N limit designed to address the competition among non-magnetic ground states. We find a rich phase diagram as a function of the filling parameter k, composed of a variety of ground states spontaneously breaking lattice symmetries, and in some cases also time reversal symmetry. One particularly striking example is a state spontaneously breaking lattice rotation symmetry, where the cubic lattice breaks up into bilayers, each of which forms a two-dimensional chiral spin liquid state.

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Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State

Abstract: We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.

Cited by 148 publications

References 32 publications

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

Coupled-wire construction of chiral spin liquids

Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions

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