Fractional topological insulators: From sliding Luttinger liquids to Chern-Simons theory

Santos, Raul A.; Huang, Chia‐Wei; Gefen, Yuval; Gutman, D. B.

doi:10.1103/physrevb.91.205141

Cited by 49 publications

(60 citation statements)

References 46 publications

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“…Naively, one would expect either one of the relevant operators g n or g ε to overtake the marginal couplings in Eqs. (39)(40)(41) and govern the low-energy physics, leading to more conventional, long-range-ordered phases. However, the fate of the system also depends on the bare values of the coupling constants, and cases in which a marginal operator reaches strong coupling before relevant ones have been discussed in the literature 61,63,64 .…”

Section: Two-dimensional Chiral Spin Liquidmentioning

confidence: 99%

“…Our approach is based on the "sliding Luttinger liquid" or "coupledwire approach" to the fractional quantum Hall effect (FQHE) 29,30 . Similar constructions based on arrays of one-dimensional (1D) subsystems have proven powerful in the description of exotic quantum Hall states and non-Abelian anyons [31][32][33][34][35][36] , fractional topological insulators [37][38][39][40] , liquids of interacting anyons 41,42 and purely 1D systems [43][44][45] .…”

Section: Introductionmentioning

confidence: 99%

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Chiral spin liquids in arrays of spin chains

2015

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We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.

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Section: Two-dimensional Chiral Spin Liquidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chiral spin liquids in arrays of spin chains

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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“…Starting with the pioneering work of Kane et al, 35,36 it has been shown that coupled-wire constructions allow for an analytically tractable description of integer and fractional, Abelian and non-Abelian topological 2D states. [37][38][39][40][41][42][43][44][45][46][47][48][49] Coupledwire constructions have also led to qualitatively new results, including a classification of interacting topological phases, 50 and the prediction of spontaneously timereversal-symmetry-broken states towards which 2D fractional topological insulators can be unstable.…”

Section: -33mentioning

confidence: 99%

“…35 It has furthermore been shown that also the Chern-Simons term associated with a 2D (fractional) quantum Hall effect is contained in the coupled-wire construction used for the individual building blocks. 47 All of these signatures combined allow to positively identify the gapped phase resulting from the coupling in Eq. (16) as an integer (for m = 0) or fractional (for integer m > 0) quantum Hall state.…”

Section: A Luttinger Liquid Description Of An Individual Building Blmentioning

confidence: 99%

Fractional topological phases in three-dimensional coupled-wire systems

Meng

2015

Phys. Rev. B

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It is shown that three-dimensional systems of coupled quantum wires support fractional topological phases composed of closed loops and open planes of two-dimensional fractional quantum Hall subsystems. These phases have topologically protected edge states, and are separated by exotic quantum phase transitions corresponding to a rearrangement of fractional quantum Hall edge modes. Some support for the existence of an extended exotic critical phase separating the bulk gapped fractional topological phases is given. Without electron-electron interactions, similar but unfractionalized bulk gapped phases based on coupled integer quantum Hall states exist. They are separated by an extended critical Weyl semimetal phase.

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Fractional topological insulators: From sliding Luttinger liquids to Chern-Simons theory

Cited by 49 publications

References 46 publications

Chiral spin liquids in arrays of spin chains

Chiral spin liquids in arrays of spin chains

Topological Floquet Phases in Driven Coupled Rashba Nanowires

Fractional topological phases in three-dimensional coupled-wire systems

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