Chiral spin liquids in arrays of spin chains

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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“…In the final stages of this work, we became aware that a similar idea is being pursued by G. Gorohovsky, R. G. Pereira, and E. Sela [52].…”

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confidence: 97%

Coupled-wire construction of chiral spin liquids

et al. 2015

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“…1), where each of them can be treated as a one-dimensional Luttinger liquid by bosonization [75][76][77][78][79][80][81][82][83][84][85][86]. This will allow us to introduce the Floquet version not only of TIs but also of Weyl semimetals in driven 2D systems.…”

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confidence: 99%

Topological Floquet Phases in Driven Coupled Rashba Nanowires

2016

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We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into nontrivial phases such as topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges e=m with m being an odd integer. DOI: 10.1103/PhysRevLett.116.176401 Introduction.-Topological effects in condensed matter systems have attracted attention for many years. From the quantum Hall effect over topological insulators (TIs) [1][2][3][4][5][6][7][8][9][10][11][12] and Weyl semimetals [13][14][15][16][17], to Majorana fermions and parafermions [39][40][41][42][43][44][45][46][47][48][49], the interest is driven both by fundamental physics and the promise for topological quantum computation. Despite the many proposals for topological systems, the search for the most optimal material still continues unabated.While most studies were focused on static structures, it has recently been proposed to extend topological phases to nonequilibrium systems, described by Floquet states . Remarkably, this approach no longer relies on given material properties, such as strong spin orbit interactions (SOIs), typically necessary for reaching topological regimes, but instead allows one to turn initially nontopological materials such as graphene [50] and non-bandinverted semiconducting wells into TIs [52] by applying an external driving field.An even bigger challenge is to describe topological effects that involve fractional excitations. This requires the presence of strong electron-electron interactions. However, given the difficulties in the search for conventional TIs, it would be even more surprising to expect such phases to occur naturally. Moreover, even if they existed, twodimensional (2D) systems with electron-electron interactions are difficult to describe analytically and often progress can come only from numerics [61].Here, we circumvent this difficulty by considering strongly anisotropic 2D systems [71][72][73][74] formed by weakly coupled Rashba wires (see Fig. 1), where each of them can be treated as a one-dimensional Luttinger liquid by bosonization [75][76][77][78][79][80][81][82][83][84][85][86]. This will allow us to introduce the Floquet version not only of TIs but also of Weyl semimetals in driven 2D systems. Importantly, in this way we can also address fractional regimes and are able to obtain the Floquet version of fractional TIs and Weyl semimetals.

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“…For λ not vanishingly small (practically, for λ > 0.01) we numerically solve both the 1st step, Eq. (51), (52), and the 2nd step, Eq. (54) and (55) as an independent parameter, there is a phase transition from SDW(z) to SDW(y) at large ratio of h x /D, and the line separating the two states tends to be horizontal as h x /D → ∞.…”

Section: F Phase Diagrammentioning

confidence: 99%

“…We hope our work will stimulate numerical studies of this interesting problem along the lines of quantum Monte-Carlo studies in Refs. 34 and 35. In concluding, we would like to mention potential relevance of our model to the currently popular coupled-wire approach to (mostly chiral) spin liquids [50][51][52] . The essence of this approach consists in devising interchain interactions in such a way as to suppress all interchain couplings between the relevant, in RG sense, degrees of freedom (such as staggered magnetization and dimerization).…”

Section: B Summary and Future Directionsmentioning

confidence: 99%

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction

Jin

Starykh²

2017

Phys. Rev. B

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Motivated by recent experiments on spin chain materials K2CuSO4Cl2 and K2CuSO4Br2, we theoretically investigate the problem of weakly coupled spin chains (chain exchange J, interchain J ) subject to a staggered between chains, but uniform within a given chain, Dzyaloshinskii-Moriya (DM) interaction of magnitude D. In the experimentally relevant limit J D J of strong DM interaction the spins on the neighboring chains are forced to rotate in opposite directions, effectively resulting in a cancelation of the interchain interaction between components of spins in the plane normal to the vector D. This has the effect of promoting two-dimensional collinear spin density wave (SDW) state, which preserves U(1) symmetry of rotations about the D-axis. We also investigate response of this interesting system to an external magnetic field h and obtain the h − D phase diagrams for the two important configurations, h D and h ⊥ D.

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Chiral spin liquids in arrays of spin chains

Cited by 76 publications

References 89 publications

Coupled-wire construction of chiral spin liquids

Coupled-wire construction of chiral spin liquids

Topological Floquet Phases in Driven Coupled Rashba Nanowires

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction

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