Charge fractionalization in nonchiral Luttinger systems

Hur, Karyn Le; Halperin, Bertrand I.; Yacoby, Amir

doi:10.1016/j.aop.2008.04.006

Cited by 46 publications

(6 citation statements)

References 45 publications

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“…For instance, the Rényi EEs can be thought of as an entanglement equivalent of the entropy of equilibrium thermodynamics, which gives an order representing the arrow of time. This has physical significance for decoherence, where entanglement with the environment plays a role [6], and in high-energy physics, where the von Neuman EE, which was first introduced within this context [7], provides quantum corrections to Hawkingʼs black hole entropy.…”

Section: Entanglement Entropies (Ees)mentioning

confidence: 99%

Entanglement entropy of non-unitary conformal field theory

Bianchini¹,

Castro-Alvaredo²,

Doyon³

et al. 2014

J. Phys. A: Math. Theor.

127

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In this letter we show that the Rényi entanglement entropy of a region of large size in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as S n ∼ c eff (n+1) 6n log , where c eff = c − 24∆ > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and ∆ = 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic (L 0 = ∆I +N with N nilpotent), then there is an additional term proportional to log(log ). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

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Section: Entanglement Entropies (Ees)mentioning

confidence: 99%

Entanglement entropy of non-unitary conformal field theory

Bianchini¹,

Castro-Alvaredo²,

Doyon³

et al. 2014

J. Phys. A: Math. Theor.

127

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show abstract

“…The plasmon scattering causes a fractionalization (cf [27,[29][30][31][32][33][34]) of the phase soliton, splitting it into an infinite series of pulses. As a result, the Fredholm determinant of a counting operator takes the form of an infinite product of determinants, each calculated for a rectangular pulse with a corresponding scattering phase δ η,n (t) = δ η,n w τ (t, 0).…”

Section: Fermi Edge Singularitymentioning

confidence: 99%

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants

Gutman¹,

Gefen²,

Mirlin³

2011

J. Phys. A: Math. Theor.

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Non-equilibrium bosonization technique facilitates the solution of a number of important manybody problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of Toeplitz type. We analyze the long time asymptotics of such determinants, using Szegő and Fisher-Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system.

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“…Spectral properties and fractionalization phenomena of 1D systems can be detected via scanning tunneling spectroscopy [80][81][82]. In particular, charge partitioning in Luttinger liquid wires [83][84][85] has been highlighted, showing that for an infinite nanotube, fractional charges can be identified through the measurement of both the autocorrelation noise and the cross correlation noise, measured at the extremities of the nanotube [86][87][88][89][90][91]. Experimental results of tunneling spectroscopy of topological insulators [92][93][94][95] have also been recently reported.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties of interacting helical channels driven by Lorentzian pulses

et al. 2019

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Precise shaping of coherent electron sources allows the controlled creation of wavepackets into a one dimensional (1D) quantum conductor. Periodic trains of Lorentzian pulses have been shown to induce minimal excitations without creating additional electron-hole pairs in a single non-interacting 1D electron channel. The presence of electron-electron (e-e) interactions dramatically affects the non-equilibrium dynamics of a 1D system. Here, we consider the intrinsic spectral properties of a helical liquid, with a pair of counterpropagating interacting channels, in the presence of timedependent Lorentzian voltage pulses. We show that peculiar asymmetries in the behavior of the spectral function are induced by interactions, depending on the sign of the injected charges. Moreover, we discuss the robustness of the concept of minimal excitations in the presence of interactions, where the link with excess noise is no more straightforward. Finally, we propose a scanning tunneling microscope setup to spectroscopically access and probe the non-equilibrium behavior induced by the voltage drive and e-e interactions. This allows a diagnosis of fractional charges in a correlated quantum spin Hall liquid in the presence of time-dependent drives.

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Charge fractionalization in nonchiral Luttinger systems

Cited by 46 publications

References 45 publications

Entanglement entropy of non-unitary conformal field theory

Entanglement entropy of non-unitary conformal field theory

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants

Spectral properties of interacting helical channels driven by Lorentzian pulses

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