Transport and scattering in inhomogeneous quantum wires

Sedlmayr, Nicholas; Ohst, Jan Peter; Affleck, Ian; Sirker, Jesko; Eggert, Sebastian

doi:10.1103/physrevb.86.121302

Cited by 24 publications

(62 citation statements)

References 46 publications

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“…For an abrupt junction [40,41], the coupling λ is proportional to the difference between the renormalized Fermi velocities on the two sides of the chain, i.e. λ ∼ (u l − u r ).…”

Section: Low-energy Limitmentioning

confidence: 99%

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Energy transport between two integrable spin chains

et al. 2016

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We study the energy transport in a system of two half-infinite XXZ chains initially kept separated at different temperatures, and later connected and let free to evolve unitarily. By changing independently the parameters of the two halves, we highlight, through bosonisation and time-dependent matrix-product-state simulations, the different contributions of low-lying bosonic modes and of fermionic quasi-particles to the energy transport. In the simulations we also observe that the energy current reaches a finite value which only slowly decays to zero. The general pictures that emerges is the following. Since integrability is only locally broken in this model, a pre-equilibration behaviour may appear. In particular, when the sound velocities of the bosonic modes of the two halves match, the low-temperature energy current is almost stationary and described by a formula with a nonuniversal prefactor interpreted as a transmission coefficient. Thermalisation, characterized by the absence of any energy flow, occurs only on longer time-scales which are not accessible with our numerics.

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“…For an abrupt junction [40,41], the coupling λ is proportional to the difference between the renormalized Fermi velocities on the two sides of the chain, i.e. λ ∼ (u l − u r ).…”

Section: Low-energy Limitmentioning

confidence: 99%

“…The perturbationV is the localised backscattering operator, responsible for reflection of fermionic waves through the junction at x = 0, and is given by [40,41] …”

Section: Low-energy Limitmentioning

confidence: 99%

Energy transport between two integrable spin chains

et al. 2016

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“…Moreover, a single TLL can have inhomogeneities: e.g., a contact between an interacting TLL and a Fermi-liquid lead, a key ingredient of most transport measurements, is often studied as an inhomogeneous TLL wire smoothly interpolating between interacting (TLL) and noninteracting (Fermi-liquid) regions or as a two-wire junction with the Luttinger parameter abruptly changing at the junction. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] A junction of three quantum wires with different Luttinger parameters has been studied in the weak coupling regime. 21,[57][58][59] The experimental importance of junctions of TLL wires with generally unequal Luttinger parameters motivates an in-depth study of their properties, which is the main objective of the present paper.…”

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confidence: 99%

Junctions of multiple quantum wires with different Luttinger parameters

et al. 2012

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Within the framework of boundary conformal field theory, we evaluate the conductance of stable fixed points of junctions of two and three quantum wires with different Luttinger parameters. For two wires, the physical properties are governed by a single effective Luttinger parameters for each of the charge and spin sectors. We present numerical density-matrix-renormalization-group calculations of the conductance of a junction of two chains of interacting spinless fermions with different interaction strengths, obtained using a recently developed method [Phys. Rev. Lett. 105, 226803 (2010)]. The numerical results show very good agreement with the analytical predictions. For three spinless wires, i.e., a Y junction, we analytically determine the full phase diagram, and compute all fixed-point conductances as a function of the three Luttinger parameters.

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“…Based on the xray edge problem, one would expect the LE to vanish with t, since local backscattering terms are inevitably induced at the boundary of the interacting region [18]. As opposed to this, we show that no OC occurs for an inhomogeneous interaction quench in one spatial dimension and the LE in the l≷v F t regions remains finite.…”

mentioning

confidence: 65%

Absence of Orthogonality Catastrophe after a Spatially Inhomogeneous Interaction Quench in Luttinger Liquids

Dóra

Pollmann²

2015

Phys. Rev. Lett.

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We investigate the Loschmidt echo, the overlap of the initial and final wave functions of Luttinger liquids after a spatially inhomogeneous interaction quench. In studying the Luttinger model, we obtain an analytic solution of the bosonic Bogoliubov-de Gennes equations after quenching the interactions within a finite spatial region. As opposed to the power-law temporal decay following a potential quench, the interaction quench in the Luttinger model leads to a finite, hardly time-dependent overlap; therefore, no orthogonality catastrophe occurs. The steady state value of the Loschmidt echo after a sudden inhomogeneous quench is the square of the respective adiabatic overlaps. Our results are checked and validated numerically on the XXZ Heisenberg chain.

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Transport and scattering in inhomogeneous quantum wires

Cited by 24 publications

References 46 publications

Energy transport between two integrable spin chains

Energy transport between two integrable spin chains

Junctions of multiple quantum wires with different Luttinger parameters

Absence of Orthogonality Catastrophe after a Spatially Inhomogeneous Interaction Quench in Luttinger Liquids

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