Spinless fermionic ladders in a magnetic field: Phase diagram

Carr, Sam T.; Narozhny, B. N.; Nersesyan, A. A.

doi:10.1103/physrevb.73.195114

Cited by 67 publications

(78 citation statements)

References 34 publications

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“…It is known that all filled states contribute to the chiral current, which is a persistent current; the chiral current in the ladder is thus generally not an infra-red phenomenon and cannot be fully accounted for by an effective lowenergy theory 34,35 . Nevertheless, certain aspects of the persistent current, such as its derivative with respect to particle number or flux, can be computed from the lowenergy theory 36 .…”

Section: Chiral Currentmentioning

confidence: 99%

Chiral currents in one-dimensional fractional quantum Hall states

2015

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We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio, ν, of particle density to magnetic flux shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic) ladders, when ν equals one over an odd (even) integer, Laughlin fractional quantum Hall (FQH) states are stabilized for sufficiently long ranged repulsive interactions. As a signature of these fractional states, we find a unique dependence of the chiral currents on particle density and on magnetic flux. This dependence is characterized by the fractional filling factor ν, and forms a stringent test for the realization of FQH states in ladders, using either numerical simulations or future ultracold-atom experiments. The two-leg model is equivalent to a single spinful chain with spin-orbit interactions and a Zeeman magnetic field, and results can thus be directly borrowed from one model to the other.

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Section: Chiral Currentmentioning

confidence: 99%

Chiral currents in one-dimensional fractional quantum Hall states

2015

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“…5) by a Bogoliubov transformation as it was previously discussed in references [72][73][74][75][76]. For convenience we transform the fermionic operators via a Fourier transformation along the legs of the ladder,…”

Section: Properties Of the Effective Fermionic Hamiltonianmentioning

confidence: 99%

Cavity-induced chiral states of fermionic quantum gases

2016

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We investigate ultra-cold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.

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“…In particular while the generic quantum phase transitions are also in the universality class of the quantum ising chain, for some special choices of parameters the symmetry associated with the quantum critical behavior is enlarged to U (1) and it is now in the universality class of a spinless Luttinger model. Two-leg ladders with flux Φ per plaquette were studied (both analytically and using numerical DMRG methods) by Roux and coworkers 39 in their work on diamagnetic effects in two-leg ladders, as well as by Carr and coworkers 40,41 who used bosonization methods to study many aspects of the phase diagram. However in their work these authors did not consider the case of flux Φ = π per plaquette in which time reversal invariance plays a key role, and the problem of PDW phases, that (as we show occur here) generically at flux Φ = π, and which is the focus of the present work.…”

Section: Introductionmentioning

confidence: 99%

Pair-density-wave superconducting order in two-leg ladders

Jaefari

Fradkin

2012

Phys. Rev. B

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We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux π per plaquette) have commensurate pair-density wave (PDW) phases. In the case of the conventional (flux-less) ladder the PDW arises when certain filling fractions for which commensurability conditions are met. For the flux π ladder the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase the uniform superconducting order parameter, the 2kF charge-densitywave (CDW) order parameter and the spin-density-wave Néel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi long range order. By making use of bosonization and the renormalization group we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the KondoHeisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.

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Spinless fermionic ladders in a magnetic field: Phase diagram

Cited by 67 publications

References 34 publications

Chiral currents in one-dimensional fractional quantum Hall states

Chiral currents in one-dimensional fractional quantum Hall states

Cavity-induced chiral states of fermionic quantum gases

Pair-density-wave superconducting order in two-leg ladders

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