Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

Das, Joy Prakash; Chowdhury, Chandramouli; Setlur, Girish S.

doi:10.1088/1402-4896/ab957f

Cited by 3 publications

(3 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our prediction is plotted in the second row of figure 2 and compared with exact numerics, which is achieved by taking advantage of the free fermionic nature of the TG limit (see appendix A for details on the implementation) which makes it possible to consider large numbers of particles and long times. The exact microscopic solution has large Friedel oscillations (cyan curve)-coming from the presence of the trap, that breaks translational invariance [61][62][63]-, which can be suppressed by spatially averaging over a small window [x − Δx/2, x + Δx/2]. After averaging, the agreement with the prediction of QGHD is remarkable.…”

Section: Results For the Density Fluctuationsmentioning

confidence: 76%

Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy

Ruggiero¹,

Calabrese²,

Doyon³

et al. 2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We apply the theory of Quantum Generalized Hydrodynamics (QGHD) introduced in [Phys. Rev. Lett. 124, 140603 (2020)] to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks-Girardeau (TG) or hard- core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher-Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.

show abstract

Section: Results For the Density Fluctuationsmentioning

confidence: 76%

Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy

Ruggiero¹,

Calabrese²,

Doyon³

et al. 2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Also it is unlikely that such numerical methods are able to capture the most singular parts of the Greenʼs functions that NCBT provides. The NCBT results have already been validated analytically using the Schwinger-Dyson equation [22] and a host of other ways as shown in our group's published works [21,23,[42][43][44][45].…”

Section: Introductionmentioning

confidence: 76%

“…But it can yield only the most singular part of the Green functions. In a recent work [23] the four-point Green functions in the context of Friedel oscillations in a Luttinger Liquid were calculated using NCBT and the most singular contribution to the slow part of the local density oscillations were obtained in the form of power laws. Closed analytical expressions for the dynamical density of states exponents were also obtained.…”

Section: Introductionmentioning

confidence: 99%

Density-density correlation function of strongly inhomogeneous Luttinger liquids

Babu¹,

Das²,

Setlur³

2020

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this work, we show in pedagogical detail that the most singular contributions to the slow part of the asymptotic density-density correlation function of Luttinger liquids with fermions interacting mutually with only short-range forward scattering and also with localised scalar static impurities (where backward scattering takes place) has a compact analytical expression in terms of simple functions that have second order poles and involve only the scale-independent bare transmission and reflection coefficients. This proof uses conventional fermionic perturbation theory resummed to all orders, together with the idea that for such systems, the (connected) moments of the density operator all vanish beyond the second order—the odd ones vanish identically and the higher order even moments are less singular than the second order moment which is the only one included. This important result is the crucial input to the recently introduced ‘Non-Chiral Bosonization Technique’ (NCBT) to study such systems. The results of NCBT cannot be easily compared with the results obtained using conventional bosonization as the former only extracts the most singular parts of the correlation functions albeit for arbitrary impurity strengths and mutual interactions. The latter, ambitiously attempts to study all the parts of the asymptotic correlation functions and is thereby unable to find simple analytical expressions and is forced to operate in the vicinity of the homogeneous system or the half line (the opposite extreme). For a fully homogeneous system or its antithesis viz. the half-line, all the higher order connected moments of the density vanish identically which means the results of chiral bosonization and NCBT ought to be the same and indeed they are.

show abstract

Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

Das

Setlur

2019

Physics Letters A

Self Cite

View full text Add to dashboard Cite

The finite-bandwidth conductance of a Luttinger liquid (LL) with a cluster of impurities is studied and its variation with respect to temperature is shown. The calculations are done using the correlation functions obtained using the powerful non-chiral bosonization technique (NCBT) . The results are compared with those obtained by Matveev, Yue and Glazman [K. Matveev et al., Phys. Rev. Lett. 71, 3351 (1993)] who deal with a weakly interacting LL. By contrast, NCBT correctly provides the conductance for all values of the interaction strength (as well as the sign). In addition to finding perfect agreement with the results of Matveev et al. for both weakly repulsive and weakly attractive mutual interactions, we are also able to probe novel physics seen when the repulsion is strong -in the form of a weakly temperature dependent conductance when there is a definite relationship between the transmission amplitude of the non-interacting system and the holon velocity. Secondly, an unusual high conductance for strongly repulsive mutual interactions is observed for a weak barrier at low temperatures. Lastly, inclusion of backward scattering leads to the non-monotonic temperature dependence of conductance when dealing with fermions with spin. This work is also important as a validation of the NCBT itself. arXiv:1809.05484v3 [cond-mat.str-el]

show abstract

Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

Cited by 3 publications

References 47 publications

Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy

Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy

Density-density correlation function of strongly inhomogeneous Luttinger liquids

Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

Contact Info

Product

Resources

About