Time-reversal symmetric hierarchy of fractional incompressible liquids

Santos, Luiz; Neupert, Titus; Ryu, Shinsei; Chamon, Claudio; Mudry, Christopher

doi:10.1103/physrevb.84.165138

Cited by 52 publications

(96 citation statements)

References 60 publications

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“…Strong intercomponent interactions in spin Hall systems may potentially lead to novel time-reversal invariant topological states (beyond simple product states) as proposed in Refs. [8,[33][34][35][36]. However, none of such phases have been found in our extensive numerical search in the present model (see Sec.…”

Section: Introductionmentioning

confidence: 87%

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Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Furukawa

Ueda

2014

Phys. Rev. A

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We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-1 2 ) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling g ↑↓ to the intracomponent one g > 0. This time-reversalinvariant setting represents a bosonic analogue of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for g ↑↓ up to as large as g. For g ↑↓ = −g, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses.

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Section: Introductionmentioning

confidence: 87%

“…Our results also indicate that in the present system, increasing g ↑↓ /g only gradually diminishes the energy gaps of such QSH states and does not lead to any novel incompressible state (beyond simple product states) proposed in Refs. [8,[33][34][35][36]. In our analysis, we set…”

Section: Exact Diagonalization Analysis For Small Filling Factorsmentioning

confidence: 99%

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Furukawa

Ueda

2014

Phys. Rev. A

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“…However, there are some additional terms which have not been previously discussed in dynamical gauge theories: the coupling to the real scalar fields φ and ψ which could be combined into a single complex scalar field. We note that this theory, unlike other hydrodynamic theories of the quantum spin Hall effect [83][84][85][86][87][88] only has a single U(1) gauge invariance (unlike the more conventional U(1)×U(1) for charge and spin). This is a natural result since in real materials spin is not conserved generically and only the local charge U(1) invariance is preserved.…”

Section: Dimensional Reductionmentioning

confidence: 99%

Effective field theories for topological insulators by functional bosonization

et al. 2013

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Effective field theories that describes the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension D = d+1 using the functional bosonization technique. For non-interacting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII) and in the "primary series" of topological insulators in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ-term (when D is even). For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these non-trivial quantum phases.

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“…Evidence for their existence has been provided in a series of analytical and numerical works in twodimensional Chern insulators [3][4][5][6][7][8][9][10][11] and time-reversal invariant topological insulators [12][13][14]. The plethora of new experimental facts and theoretical ideas discovered in the non-interacting topological insulators suggests that their fractional (i.e.…”

Section: Introductionmentioning

confidence: 99%

D-algebra structure of topological insulators

2012

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In the quantum Hall effect, the density operators at different wave-vectors generally do not commute and give rise to the Girvin MacDonald Plazmann algebra with important consequences such as ground-state center of mass degeneracy at fractional filling fraction, and W1+∞ symmetry of the filled Landau levels. We show that the natural generalization of the GMP algebra to higher dimensional topological insulators involves the concept of a D-commutator. For insulators in even dimensional space, the D-commutator is isotropic and closes, and its structure factors are proportional to the D/2-Chern number. In odd dimensions, the algebra is not isotropic, contains the weak topological insulator index (layers of the topological insulator in one less dimension) and does not contain the Chern-Simons θ form. This algebraic structure paves the way towards the identification of fractional topological insulators through the counting of their excitations. The possible relation to D-dimensional volume preserving diffeomorphisms and parallel transport of extended objects is also discussed.

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Time-reversal symmetric hierarchy of fractional incompressible liquids

Cited by 52 publications

References 60 publications

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Effective field theories for topological insulators by functional bosonization

D-algebra structure of topological insulators

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