Quantum Field Theory of Many-Body Systems

Wen, Xiao-Gang

doi:10.1093/acprof:oso/9780199227259.001.0001

Cited by 1,138 publications

(2,160 citation statements)

References 41 publications

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“…The FQH state is often called topologically ordered. Topological orders are general properties of many-body quantum states at zero temperature, which have a non-zero energy gap between the ground state and excited states (Wen 2004) Most ordered phases occur on lowering the temperature of a system, and thus forcing it through a thermal phase transition that occurs at a critical temperature T c . In contrast to a thermal phase transition, a quantum phase transition (Sachdev 2011) takes place at T = 0 and is caused by the change of another parameter such as applied magnetic field or pressure.…”

Section: Order In the Fqh Statesmentioning

confidence: 99%

“…(It is worth noting that this doesn't imply the FQHE is only observed at the inaccessible temperature T=0, although it is observed exclusively at low (usually milliKelvin) temperatures.) Moreover, although most phase transitions involve a lowering of the symmetry of a state, the FQH states all have the same symmetry, despite having different values of ν (Wen 2004). …”

Section: Order In the Fqh Statesmentioning

confidence: 99%

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Reduction and emergence in the fractional quantum Hall state

Lancaster

Pexton

2015

Studies in History and Philosophy of Science Part B: Studies in

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Section: Order In the Fqh Statesmentioning

confidence: 99%

Section: Order In the Fqh Statesmentioning

confidence: 99%

Reduction and emergence in the fractional quantum Hall state

Lancaster

Pexton

2015

Studies in History and Philosophy of Science Part B: Studies in

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“…When applied to elections in the (lowest) Landau level, this approach is equivalent to the composite particle (composite boson and composite fermion) theories. 23,[28][29][30][31][32][89][90][91][92][93][94] The functional bosonization is also readily applicable to fractional quantum Hall states formed on a lattice, i.e., "fractional Chern insulators". See Refs.…”

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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“…(21), (24), and (28) are felt by the c fermions and lead to residual interactions between those and the s1 fermions, whose effective interaction energy is derived in Ref. 28 .…”

Section: The Extended Jordan-wigner Transformationmentioning

confidence: 99%

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Carmelo

2010

Nuclear Physics B

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The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one-and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U (1) symmetry. For the model in the oneand two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one-and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U/4t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field Bs1 ex 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N/2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U/4t finite the degeneracy of the N/2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by Bs1 L 2 /Φ0 and the s1 effective lattice spacing by as1 = ls1/ √ 2π where ls1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ0 = 1. Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.

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Quantum Field Theory of Many-Body Systems

Cited by 1,138 publications

References 41 publications

Reduction and emergence in the fractional quantum Hall state

Reduction and emergence in the fractional quantum Hall state

Effective field theories for topological insulators by functional bosonization

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

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