Quantum Phase Transitions in Bilayer Quantum Hall Systems at a Total Filling Factor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ν</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>

Ye, Jinwu; Jiang, Longhua

doi:10.1103/physrevlett.98.236802

Cited by 30 publications

(27 citation statements)

References 37 publications

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“…Conversely, for small enough spacing between the two layers the ground state is known to be the interlayer coherent "111 state", which we can think of as a composite boson (CB), or interlayer exciton condensate, 4 with strong interlayer correlations and intralayer correlations which are weaker than those of the composite fermion Fermi sea. 1 While the nature of these two limiting states is reasonably well understood, the nature of the states at intermediate d is less understood and has been an active topic of both theoretical 3,5,6,7,8,9,10,11,12,13,14,15,16 and experimental interest. 17,18,19,20,21,22,23,24,25,26,27 Although there are many interesting questions remaining that involve more complicated experimental situations, within the current work we always consider a zero temperature bilayer system with zero tunnelling between the two layers and no disorder.…”

Section: Introductionmentioning

confidence: 99%

“…Some very influential works have pointed to the possibility that a number of exotic phases could be lurking within this transition as well. 3,9,10,11,14,31 In particular, it has been suggested 3,11,12 that the bilayer CF Fermi sea is always unstable to BCS pairing from weak interactions between the two layers (due to gauge field fluctuations). Some of these works 11,12 further concluded that the pairing of CFs should be in the p x − ip y channel, which would be analogous to the pairing that occurs in single layer CF systems to form the Moore-Read Pfaffian state 32,33 from the CF Fermi sea.…”

Section: Introductionmentioning

confidence: 99%

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Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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Quantum Hall bilayer systems at filling fractions near ν = 1 2 + 1 2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wavefunctions. We consider two main classes of wavefunctions. In the first class, previously introduced in Möller et al. (2003)] and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of d ℓ 0 , as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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“…The q eigenstates χ l ; l = 0, 1, · · · , q − 1 which forms a q dimensional representation of the magnetic space group ( MSG ) [38] can be written as χ l ( x) = 1 √ N q−1 m=0 c m ω −ml e i2πf (mx+ly) where x = (x, y). Then expand the vortex operator ψ( x) = q−1 l=0 φ l ( x)χ l ( x) where φ l ( x) are the q order parameters.…”

Section: Discussionmentioning

confidence: 99%

Quantum phases, supersolids and quantum phase transitions of interacting bosons in frustrated lattices

Chen

2013

Nuclear Physics B

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By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from 1/3 ( 2/3 ) filling on frustrated lattices such as triangular and kagome lattice. In a triangular lattice at 1/3, we find a X-CDW, a stripe CDW phase which was found perviously by a density operator formalism (DOF). Most importantly, we also find a new CDW-VB phase which has both local CDW and local VB orders, in sharp contrast to a bubble CDW phase found previously by the DOF. In the Kagome lattice at 1/3, we find a VBS phase and a 6 fold-CDW phase. Most importantly, we also identify a CDW-VB phase which has both local CDW and local VB orders which was found in previous QMC simulations. We also study several other phases which are not found by the DVM. By analyzing carefully the saddle point structures of the dual gauge fields in the translational symmetry breaking sides and pushing the effective actions slightly away from the commensurate filling f = 1/3( 2/3 ), we classified all the possible types of supersolids and analyze their stability conditions. In a triangular lattice, there are X-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid ( VB-SS ). There are also a new kind of supersolid: CDW-VB supersolid. In a Kagome lattice, there are 6 fold-CDW supersolid, stripe CDW supersolid, but absence of any valence bond supersolid ( VB-SS ). There are also a new kind of supersolid: CDW-VB supersolid. We show that independent of the types of the SS, the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents z = 2, ν = 1/2, η = 0 ( with logarithmic corrections ). Excitation spectra of all these insulating phases and supersolid phases are also studied. Implications on QMC simulations with both nearest neighbor and next nearest neighbor interactions in both lattices are given. Some possible intrinsic problems of the DOF in identifying the insulating phases are also pointed out.

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“…When δ T− < 0, it is in the stripe SSDW state where φ − = φ 0 e −i(QT z+θ) . It is a first order quantum Lifshitz type of transition [38][39][40][41][42], so the dynamic exponent z can not be defined. This is in sharp contrast to the second order transition with the z = 3 (FM) or z = 2 (AFM) in the Hertz-Millis action Eqn.B1 to describe magnetic phase transitions in itinerant electron systems without SOC.…”

Section: Quantum Lifshitz Transition From the Paramagnet To Ssdw Tmentioning

confidence: 99%

“…This maybe the first quantum Lifshitz transition in any itinerant Fermi systems. Similar types of bosonic Lifshitz transition exist in various condensed matter systems such as the superfluid 4 He [40], exciton superfluids in bilayer quantum Hall or electron-hole bilayer [41] and superconductor in a Zeeman field [38,42]. We analyze the symmetry breaking pattern of the SSDW and work out its one gapless spinlattice coupled Goldstone mode.…”

Section: Introductionmentioning

confidence: 99%

Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

Zhang

Liu

2016

Phys. Rev. B

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Magnetic phenomena in itinerant electron systems has been at the forefront in material science. Here we show that the Weyl spin-orbit couplings (SOC) in 3 dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations and phase transitions. A putative Ferromagnetic state (FM) is always unstable against a stripe Spiral spin density wave (S-SDW) or a stripe Longitudinal-SDW at small or large SOC strengths respectively. The stripe ordering wavevector is given by the nesting momentum of the two SOC split Fermi surfaces with the same or opposite helicities at small or large SOC strengths respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and FS re-constructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold atom experiments are briefly discussed. In view of recent groundbreaking experimental advances in generating 2d SOC in cold atoms, these phenomena can be observed in current or near future cold atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.

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Quantum Phase Transitions in Bilayer Quantum Hall Systems at a Total Filling FactorνT=1

Cited by 30 publications

References 37 publications

Trial wave functions forν=12+12quantum Hall bilayers

Trial wave functions forν=12+12quantum Hall bilayers

Quantum phases, supersolids and quantum phase transitions of interacting bosons in frustrated lattices

Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

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