Showing papers on "Luttinger parameter published in 2020"
TL;DR: For the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one.
Abstract: In spin chains with local unitary evolution preserving the magnetization ${S}^{\mathrm{z}}$, the domain-wall state $\left|\ensuremath{\cdots}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\cdots}\right\ensuremath{\rangle}$ typically ``melts.'' At large times, a nontrivial magnetization profile develops in an expanding region around the initial position of the domain wall. For nonintegrable dynamics, the melting is diffusive, with entropy production within a melted region of size $\sqrt{t}$. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: The spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasiparticle charge (or Luttinger parameter $K$), which acquires a fractal dependence on the XXZ chain anisotropy parameter $\mathrm{\ensuremath{\Delta}}$.
28 citations
TL;DR: In this article, a general framework is developed to compute the scaling of entanglement entropy in inhomogeneous one-dimensional quantum systems belonging to the Luttinger liquid universality class.
Abstract: We develop a general framework to compute the scaling of entanglement entropy in inhomogeneous one-dimensional quantum systems belonging to the Luttinger liquid universality class. While much insight has been gained in homogeneous systems by making use of conformal field theory techniques, our focus is on systems for which the Luttinger parameter K depends on position, and conformal invariance is broken. An important point of our analysis is that contributions stemming from the UV cutoff have to be treated very carefully, since they now depend on position. We show that such terms can be removed either by considering regularized entropies specifically designed to do so, or by tabulating numerically the cutoff, and reconstructing its contribution to the entropy through the local density approximation. We check our method numerically in the spin-1/2 XXZ spin chain in a spatially varying magnetic field, and find excellent agreement.
19 citations
TL;DR: In this paper, the Andreev-Bashkin collisionless drag for a two-component onedimensional Bose-Hubbard model on a ring was theoretically investigated, and the most promising region close to the so-called pair-superfluid phase was observed, where the drag can become comparable with the total superfluid density.
Abstract: We theoretically investigate the elusive Andreev-Bashkin collisionless drag for a two-component onedimensional Bose-Hubbard model on a ring. By means of tensor network algorithms, we calculate the superfluid stiffness matrix as a function of intra- and interspecies interactions and of the lattice filling. We then focus on the most promising region close to the so-called pair-superfluid phase, where we observe that the drag can become comparable with the total superfluid density. We elucidate the importance of the drag in determining the long-range behavior of the correlation functions and the spin speed of sound. In this way, we are able to provide an expression for the spin Luttinger parameter $K_S$ in terms of drag and the spin susceptibility. Our results are promising in view of implementing the system by using ultracold Bose mixtures trapped in deep optical lattices, where the size of the sample is of the same order of the number of particles we simulate. Importantly, the mesoscopicity of the system, far from being detrimental, appears to favor a large drag, avoiding the Berezinskii-Kosterlitz-Thouless jump at the transition to the pair-superfluid phase which would reduce the region where a large drag can be observed.
17 citations
TL;DR: The glassy properties of the Bose-glass phase are revealed and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
Abstract: We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
11 citations
TL;DR: In this paper, the edge current in the charge Kondo circuit was investigated in the integer quantum Hall regime, where the quantum dot (QD) coupled weakly to an electrode at temperature T + Δ T and connected strongly to another electrode at the reference temperature T by a single-mode quantum point contact (QPC).
Abstract: We investigate theoretically quantum transport through the "charge" Kondo circuit consisting of the quantum dot (QD) coupled weakly to an electrode at temperature $T+\Delta T$ and connected strongly to another electrode at the reference temperature $T$ by a single-mode quantum point contact (QPC). To account for the effects of Coulomb interaction in the QD-QPC setup operating in the integer quantum Hall regime we describe the edge current in the quantum circuit by Luttinger model characterized by the Luttinger parameter $g$. It is shown that the temperature dependence of both electric conductance $G\propto T^{2/g}$ and thermoelectric coefficient $G_T\propto T^{1+2/g}$ detours from the Fermi-liquid (FL) theory predictions. The behaviour of the thermoelectric power $S=G_T/G\propto T$ in a regime of a single-channel Kondo effect is, by contrast, consistent with the FL paradigm. We demonstrate that the interplay between the mesoscopic Coulomb blockade in QD and weak repulsive interaction in the Luttinger Liquid $g=1-\alpha$ $(\alpha \ll 1)$ results in the enhancement of the thermopower. This enhancement is attributed to suppression of the Kondo correlations in the "charge" circuit by the destructive quantum interference effects.
6 citations
TL;DR: In this paper, the four-point Green functions relevant to the study of Friedel oscillations are calculated for a Luttinger liquid (LL) with a cluster of impurities around an origin using the recently developed non-chiral bosonization technique (NCBT).
Abstract: In this work, the four-point Green functions relevant to the study of Friedel oscillations are calculated for a Luttinger liquid (LL) with a cluster of impurities around an origin using the recently developed non-chiral bosonization technique (NCBT). Analytical expressions are obtained for the most singular part of the envelope of the oscillatory part of the local density in the form of power laws, providing closed expressions for the governing exponents. A comparison is done with the work of Egger and Grabert and an exact match of the exponent is obtained both for points near and far from the impurity. The two-point functions (most singular part) obtained using the same method are used to calculate the dynamical density of states (DDOS), which exhibits a power law in energy and closed analytical expressions for the DDOS exponent is calculated. These results interpolates between the weak barrier and weak link cases which are typically studied in the literature. The dependence of the DDOS on the nature of interactions and the strength of the impurity clusters are highlighted. Finally, the results of DDOS are favorably compared with existing literature such as density of states far away and near the impurity. We also compare with the often studied special case when the Luttinger parameter g=1/2 and find agreement with our results for strong barriers.
4 citations
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TL;DR: In this paper, the equivalence between two distinct Luttinger liquid impurity problems is demonstrated, and it is shown that the non-trivial intermediate critical points are the same.
Abstract: We demonstrate the equivalence between two distinct Luttinger liquid impurity problems. The first concerns a one-dimensional topological superconductor coupled at one end to the ends of two single channel Luttinger liquids. The second concerns a point contact in the quantum spin Hall effect, where four helical Luttinger liquids meet at a point. Both problems have been studied previously and exhibit several stable phases depending on the Luttinger parameter K, that can be characterized in terms of simple conformally invariant boundary conditions describing perfect normal (or Andreev) transmission or reflection. In addition, both problems exhibit critical points that are described by "intermediate" fixed points similar to those found in earlier studies of an impurity in a Luttinger liquid with spin. Though these two models have different symmetries and numbers of modes, we show they are equivalent and are related by a duality transformation, and we show that the non-trivial intermediate critical points are the same. In the non-interacting limit, K=1, the duality involves two distinct free fermion representations that are related by a non-local transformation that derives from the triality of SO(8). Using the explicit translation between the two theories, we translate results from one problem to the other and vice versa. This allows us to make new predictions about the topological superconductor-Luttinger liquid junction, including predictions about the global behavior of the critical conductance G*(K), as well predictions for the critical exponents and universal crossover scaling functions. In this paper we introduce both models from scratch, using a common notation that facilitates their comparison, and we discuss in detail the dualities that relate them, along with their free fermion limits. We close with a discussion of open problems and future directions.
4 citations
TL;DR: In this article, the effects of a periodically driven Rashba impurity at the helical edge, in the presence of electron-electron interactions, were analyzed by means of bosonization, and the backscattering current was computed perturbatively up to second order in the impurity strength.
Abstract: The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single-particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is visible only if processes that do not conserve the single-particle energy are included. Paradigmatic examples of such processes are electron-electron interactions and time-dependent external drivings. We analyze the effects of a periodically driven Rashba impurity at the helical edge, in the presence of electron-electron interactions. Interactions are treated by means of bosonization, and the backscattering current is computed perturbatively up to second order in the impurity strength. We show that the backscattering current is nonmonotonic in the driving frequency. This property is a fingerprint of the Rashba impurity, being absent in the case of a magnetic impurity in the helical liquid. Moreover, the nonmonotonic behavior allows us to directly link the backscattering current to the Luttinger parameter $K$, encoding the strength of electron-electron interactions.
4 citations
TL;DR: Dupont et al. as discussed by the authors test the analytical formula for the enhancement of the nuclear magnetic resonance rate by the critical spin fluctuations, over the simple power-law dependence predicted for a purely one-dimensional spin system, recently derived in the random phase approximation.
Abstract: We test the analytical formula for the enhancement of the nuclear magnetic resonance rate ${T}_{1}^{\ensuremath{-}1}$ by the critical spin fluctuations, over the simple power-law dependence predicted for a purely one-dimensional spin system, recently derived in the random phase approximation [M. Dupont et al., Phys. Rev. B 98, 094403 (2018)]. This prediction is experimentally confirmed by excellent fits to the published temperature dependence of ${T}_{1}^{\ensuremath{-}1}$ data in the two representative spin compounds, ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ (DIMPY) and ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, providing at the same time a direct and convenient experimental determination of the Tomonaga-Luttinger-liquid parameter $K$, very well in agreement with theoretical predictions.
4 citations
TL;DR: In this paper, the two-pulse spin-dependent photon echo technique was used to study the in-plane hole spin anisotropy in a 20nm-thick CdTe/Cd$_{0.76}$Mg${0.24}$Te single quantum well by exciting the donor-bound exciton resonance.
Abstract: We use the two-pulse spin-dependent photon echo technique to study the in-plane hole spin anisotropy in a 20~nm-thick CdTe/Cd$_{0.76}$Mg$_{0.24}$Te single quantum well by exciting the donor-bound exciton resonance. We take advantage of the photon echo sensitivity to the relative phase of the electron and hole spin precession and study various interactions contributing to the hole in-plane spin properties. The main contribution is found to arise from the crystal cubic symmetry described by the Luttinger parameter $q=0.095$, which is substantially larger than the one theoretically expected for CdTe or found in other quantum well structures. Another contribution is induced by the strain within the quantum well. These two contributions manifest as different harmonics of the spin precession frequencies in the photon echo experiment, when strength and orientation of the Voigt magnetic field are varied. The magnitude of the effective in-plane hole $g$ factor is found to vary in the range $|\tilde{g_h}|$=0.125--0.160 in the well plane.
2 citations
TL;DR: In this article, the edge current in the charge Kondo circuit was investigated in the integer quantum Hall regime, where the quantum dot (QD) coupled weakly to an electrode at temperature T + Δ T and connected strongly to another electrode at the reference temperature T by a single-mode quantum point contact (QPC).
Abstract: We investigate theoretically quantum transport through the "charge" Kondo circuit consisting of the quantum dot (QD) coupled weakly to an electrode at temperature $T+\Delta T$ and connected strongly to another electrode at the reference temperature $T$ by a single-mode quantum point contact (QPC). To account for the effects of Coulomb interaction in the QD-QPC setup operating in the integer quantum Hall regime we describe the edge current in the quantum circuit by Luttinger model characterized by the Luttinger parameter $g$. It is shown that the temperature dependence of both electric conductance $G\propto T^{2/g}$ and thermoelectric coefficient $G_T\propto T^{1+2/g}$ detours from the Fermi-liquid (FL) theory predictions. The behaviour of the thermoelectric power $S=G_T/G\propto T$ in a regime of a single-channel Kondo effect is, by contrast, consistent with the FL paradigm. We demonstrate that the interplay between the mesoscopic Coulomb blockade in QD and weak repulsive interaction in the Luttinger Liquid $g=1-\alpha$ $(\alpha \ll 1)$ results in the enhancement of the thermopower. This enhancement is attributed to suppression of the Kondo correlations in the "charge" circuit by the destructive quantum interference effects.