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arXiv:1907.07090 · Physical review. B./Physical review. B

Ion-induced interactions in a Tomonaga-Luttinger liquid

Andreas Bock Michelsen, Manuel Valiente, Nikolaj Thomas Zinner, Antonio Negretti

Published Nov 27, 2019• 9 citations
arXivHTMLPDF

Abstract

We investigate the physics of a Tomonaga-Luttinger liquid of spin-polarized fermions superimposed on an ion chain. This compound system features (attractive) long-range interspecies interactions. By means of density matrix renormalization group techniques we compute the Tomonaga-Luttinger-liquid parameter and speed of sound as a function of the relative atom/ion density and the two quantum defect parameters, namely, the even and odd short-range phases which characterize the short-range part of the atom-ion polarization potential. The presence of ions is found to allow critical tuning of the atom-atom interaction, and the properties of the system are found to depend significantly on the short-range phases due to the atom-ion interaction. These latter dependencies can be controlled, for instance, by manipulating the ions' internal state. This allows modification of the static properties of the quantum liquid via external driving of the ionic impurities.

DOI
10.1103/physrevb.100.205427

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•Sep 27, 2019•0 citations
We investigate the physics of a Tomonaga-Luttinger liquid of spin-polarized fermions superimposed on an ion chain. This compound system features (attractive) long-range interspecies interactions. By means of density matrix renormalization group techniques we compute the Tomonaga-Luttinger-liquid parameter and speed of sound as a function of the relative atom/ion density and the two quantum defect parameters, namely, the even and odd short-range phases which characterize the short-range part of the atom-ion polarization potential. The presence of ions is found to allow critical tuning of the atom-atom interaction, and the properties of the system are found to depend significantly on the short-range phases due to the atom-ion interaction. These latter dependencies can be controlled, for instance, by manipulating the ions' internal state. This allows modification of the static properties of the quantum liquid via external driving of the ionic impurities.
Quantum fluctuations can disrupt long-range order in one-dimensional systems and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasiadiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.
The characterization of quantum spin liquid phases in Kitaev materials has been a subject of intensive studies over the recent years, both theoretically and experimentally. Most theoretical studies have focused on an isotropically interacting model with its coupling strength being equivalent on each bond in an attempt to simplify the problem. In this Letter, we study an extended spin-1/2 Kitaev- Γ model on a honeycomb lattice with an additional tuning parameter that controls the coupling strength on one of the bonds: We connect the limit of isolated Kitaev- Γ chains, which is known to exhibit an emergent S U ( 2 ) 1 Tomonaga-Luttinger liquid phase [Yang , ], to the two-dimensional model. We report on an instance, in which properties of the Tomonaga-Luttinger liquid persist for finite interchain coupling forming a phase we call the proximate Tomonaga-Luttinger liquid (pTLL). This pTLL is strongly anisotropic in character analogous to , and features spinon-like excitations similar to those of the antiferromagnetic Heisenberg chain. We use numerical exact diagonalization and density matrix renormalization group on various cluster geometries in a complementary way to overcome finite-size limitations. Published by the American Physical Society 2024
An impurity in a Tomonaga-Luttinger liquid leads to a crossover between the short- and long-distance regime which describes many physical phenomena. However, a calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on the infinite density matrix renormalization group. By utilizing infinite boundary conditions we can obtain correlation functions within a finite-size window that contains the impurity. For the S=1/2S=1/2S=1/2 chain, we demonstrate that a full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with field-theory predictions.
Abstract Long-range interactions in one-dimensional quantum systems can qualitatively modify low-energy critical behavior and provide a natural setting for exploring unconventional phase transitions beyond short-range Tomonaga—Luttinger liquid physics. In this work, we study a one-dimensional XXZ spin chain with transverse long-range interactions and an explicit dimerization perturbation. Using bosonization and weak-coupling renormalization group (RG) analysis, we derive the RG flow equations. The resulting weak-coupling phase diagram contains a gapless Tomonaga—Luttinger liquid, an explicitly dimerized phase, and a continuous symmetry breaking (CSB) phase induced by the transverse long-range interaction. We further analyze the collapse point at which the two perturbations become simultaneously marginal. A stability analysis of the corresponding doubly marginal Gaussian fixed point shows that it is weakly unstable rather than a stable multicritical infrared fixed point, thereby giving rise to a pseudo-multicritical crossover over large length scales. Similar physics may be accessible in Rydberg-atom systems, offering a controllable theoretical and experimental platform for exploring long-range interaction effects and crossover behavior in one-dimensional quantum systems.
The formation of bound states of fermions in one dimension has always been one of the key topics in condensed matter physics. Motivated by recent experimental progresses in Prof. Jeremy Levy's group, we study the interplay of both species (spin and transverse band index) and mass imbalance in a mixture of two or more species of fermions with attractive interactions in one dimension. Previous theoretical and experimental efforts have shown the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase for the case of two species with equal mass, in addition to the fully paired and fully polarized phases. For the unequal mass case, there are signatures of trion phases as well. We use DMRG to explore the rich possibilities of quantum phases and their transport signatures for the cases of two and more species of Fermions as we vary the interaction strengths and mass imbalances. With this we can gain insights into ongoing experiments with sketched nanowires in LAO/STO and ultracold atoms confined to one-dimensional tubes. We also study the formation of bound states in a single component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one emergent neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.