Pokrovsky-Talapov model at finite temperature: A renormalization-group analysis

Lazarides, Achilleas; Tieleman, O.; Smith, C. Morais

doi:10.1103/physrevb.80.245418

Cited by 9 publications

(17 citation statements)

References 39 publications

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“…6. Columns (1) and (2). Spatial profile of the density fluctuations determined from the Bogoliubov calculation for each mode.…”

Section: Bogoliubov Theorymentioning

confidence: 99%

“…where E (•) is the complete elliptic integral of the second kind, and the integration constant C has yet to be determined. The location of the critical point Q c can be calculated determining when the "chemical potential" Q makes the solitonic configuration energetically favouable [2]: normally the energy of a soliton is higher than the minimal energy configuration, E n = 0, of a sine-Gordon field theory, corresponding to n = 2nπ (field pinned at the minima of the cosine). This excess of energy can be compensated by the Pokrovsky-Talapov misfit, Q; analogously to a chemical potential, it can lower the energy of a soliton, which can become a favorable energy configuration when its energy equals that one of the field in the commensurate phase.…”

Section: Q and Location Of The Critical Pointmentioning

confidence: 99%

“…By changing Q one can modify the length between two adjacent solitons l Q ∝ 1/Q, see Refs. [1,2]. model with competing interactions, type-II superconductors, quantum Hall bilayer systems under a tilted magnetic field [17][18][19][20][21], and the transition from zero to finite momentum pairing in two-component attractive fermions in presence of a Zeeman field [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…The spatial modulation corresponds to a situation in which upon tunneling atoms acquire a finite momentum along the direction of the tubes. This modification enlarges the potential of one-dimensional Bose gases on atom chips as quantum simulators: imprinting a phase winding on the tunneling process constitutes a realization of the Pokrovsky-Talapov (PT) model [1,2,16,[28][29][30][31][32][33][34][35]. This is a variant of the sine-Gordon field theory, which hosts a commensurate-incommensurate transition between a homogeneous and inhomogeneous phase.…”

Section: Introductionmentioning

confidence: 99%

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Simulating a quantum commensurate-incommensurate phase transition using two Raman-coupled one-dimensional condensates

Kasper

Marino

et al. 2020

Phys. Rev. B

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We study a transition between a homogeneous and an inhomogeneous phase in a system of one-dimensional, Raman tunnel-coupled Bose gases. The homogeneous phase shows a flat density and phase profile, whereas the inhomogeneous ground state is characterized by periodic density ripples and a soliton staircase in the phase difference. We show that under experimentally viable conditions the transition can be tuned by the wave-vector difference Q of the Raman beams and can be described by the Pokrovsky-Talapov model for the relative phase between the two condensates. Local imaging available in atom chip experiments allows us to observe the soliton lattice directly, while modulation spectroscopy can be used to explore collective modes, such as the phonon mode arising from breaking of translation symmetry by the soliton lattice. In addition, we investigate regimes where the cold atom experiment deviates from the Pokrovsky-Talapov field theory. We predict unusual mesoscopic effects arising from the finite size of the system, such as quantized injection of solitons upon increasing Q, or the system size. For moderate values of Q above criticality, we find that the density modulations in the two gases interplay with the relative phase profile and introduce novel features in the spatial structure of the mode wave functions. Using an inhomogeneous Bogoliubov theory, we show that spatial quantum fluctuations are intertwined with the emerging soliton staircase. Finally, we comment on the prospects of the ultracold atom setup.

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“…6. Columns (1) and (2). Spatial profile of the density fluctuations determined from the Bogoliubov calculation for each mode.…”

Section: Bogoliubov Theorymentioning

confidence: 99%

Section: Q and Location Of The Critical Pointmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulating a quantum commensurate-incommensurate phase transition using two Raman-coupled one-dimensional condensates

Kasper

Marino

et al. 2020

Phys. Rev. B

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show abstract

“…In every step, an infinitesimal part of the integration is carried out, yielding an effective energy functional at an infinitesimally lower momentum scale or cutoff. By computing the change in the parameters in the energy functional under an infinitesimal change in the cutoff, one obtains the flow equations for s and t. 16 Integrating these equations over the cutoff running from its initial value to zero, one obtains an effective energy functional EЈ͓͔ for which we have…”

Section: Finite Temperaturementioning

confidence: 99%

Bilayer quantum Hall system atνt=1: Pseudospin models and in-plane magnetic field

Tieleman¹,

Lazarides²,

Makogon³

et al. 2009

Phys. Rev. B

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We investigate two theoretical pseudomagnon-based models for a bilayer quantum Hall system ͑BQHS͒ at total filling factor t = 1. We find a unifying framework which elucidates the different approximations that are made. We also consider the effect of an in-plane magnetic field in BQHSs at t = 1, by deriving an equation for the ground-state energy from the underlying microscopic physics. Although this equation is derived for small in-plane fields, its predictions agree with recent experimental findings at stronger in-plane fields, for low electron densities. We also take into account finite-temperature effects by means of a renormalization group analysis, and find that they are small at the temperatures that were investigated experimentally.

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Strongly interacting bosons in a one-dimensional optical lattice at incommensurate densities

2011

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We investigate quantum phase transitions occurring in a system of strongly interacting ultracold bosons in a 1D optical lattice. After discussing the commensurate-incommensurate transition, we focus on the phases appearing at incommensurate filling. We find a rich phase diagram, with superfluid, supersolid and solid (kink-lattice) phases. Supersolids generally appear in theoretical studies of systems with long-range interactions; our results break this paradigm and show that they may also emerge in models including only short-range (contact) interactions, provided that quantum fluctuations are properly taken into account. PACS numbers:The rapid progress in trapping and cooling atoms has rendered the study of "tailor-made" low-dimensional (D) systems [1] experimentally accessible. Both the dimensionality and the interactions can be controlled, allowing great flexibility in realizing almost arbitrary stronglycorrelated physical systems. A superfluid-Mott insulator (SF-MI) quantum phase transition, driven by increasing the potential depth of the optical lattice (and hence the relative strength of interactions) beyond a critical value, has been observed for bosons loaded into an optical lattice in 3D [2], 2D [3], and 1D [4]. In addition, the Tonks-Girardeau gas, where bosons avoid spatial overlap and acquire fermionic properties due to strong repulsive interactions, has been experimentally realized in 1D [5].Recently, a new type of quantum phase transition was observed in 1D in the very strongly interacting regime: for an arbitrarily weak optical lattice potential commensurate with the atomic density of the Bose gas, a quantum phase transition into an insulating, gapped state, was observed, with the atoms pinned at the lattice minima [6]. Theoretical studies of 1D systems based on the sine-Gordon model indeed predict that above a critical interaction strength, the SF should become a MI even for a vanishingly weak optical lattice [7].

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Pokrovsky-Talapov model at finite temperature: A renormalization-group analysis

Cited by 9 publications

References 39 publications

Simulating a quantum commensurate-incommensurate phase transition using two Raman-coupled one-dimensional condensates

Simulating a quantum commensurate-incommensurate phase transition using two Raman-coupled one-dimensional condensates

Bilayer quantum Hall system atνt=1: Pseudospin models and in-plane magnetic field

Strongly interacting bosons in a one-dimensional optical lattice at incommensurate densities

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