Platforms for the realization and characterization of Tomonaga-Luttinger liquids
arXiv:2501.12097 · doi:10.1038/s42254-025-00866-w
Abstract
The concept of a Tomonaga-Luttinger liquid (TLL) has been established as a fundamental theory for the understanding of one-dimensional quantum systems. Originally formulated as a replacement for Landau's Fermi-liquid theory, which accurately predicts the behaviour of most 3D metals but fails dramatically in 1D, the TLL description applies to a even broader class of 1D systems,including bosons and anyons. After a certain number of theoretical breakthroughs, its descriptive power has now been confirmed experimentally in different experimental platforms. They extend from organic conductors, carbon nanotubes, quantum wires, topological edge states of quantum spin Hall insulators to cold atoms, Josephson junctions, Bose liquids confined within 1D nanocapillaries and spin chains. In the ground state of such systems, quantum fluctuations become correlated on all length scales, but, counter-intuitively, no long-range order exists. In this respect, this review will illustrate the validity of conformal field theory for describing real-world systems, establishing the boundaries for its application and, on the other side will discuss the spectacular demonstration of how the quantum-critical TLL state governs the properties of many-body systems in one dimension.
arXiv commentBrief review of Tomonaga-Luttinger liquid physics and its experimental realizations. (RevTeX4.2, 22 pages, 6 figures) (v2) title changed, some references added
References in corpus (136)
- Quantum Spin Hall Effect in Graphene
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- New directions in the pursuit of Majorana fermions in solid state systems
- Quantized Anomalous Hall Effect in Magnetic Topological Insulators
- Luttinger Liquid Behavior in Carbon Nanotubes
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Topological orders and Edge excitations in FQH states
- Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm
- Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
- Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
- Higher-Order Topology in Bismuth
- Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- The Helical Liquid and the Edge of Quantum Spin Hall Systems
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Edge conduction in monolayer WTe2
- Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
- One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
- Spontaneous Quantum Hall States in Chirally-stacked Few-Layer Graphene Systems
- One-dimensional Topological Edge States of Bismuth Bilayers
- Spin-charge separation and localization in one-dimension
- Coupled Ladders in a Magnetic Field
- Quantum criticality and universal scaling of a quantum antiferromagnet
- Generalized HydroDynamics on an Atom Chip
- Topological phases with parafermions: theory and blueprints
- Kondo effect in the helical edge liquid of the quantum spin Hall state
- Probing spin-charge separation in a Tomonaga-Luttinger liquid
- Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
- Electric Field-Tuned Topological Phase Transition in Ultra-Thin Na3Bi - Towards a Topological Transistor
- Critical Properties of gapped spin-1/2 chains and ladders in a magnetic field
- Quantum Theory of the Smectic Metal State in Stripe Phases
- Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
- Controlling Luttinger liquid physics in spin ladders under a magnetic field
- Generalized hydrodynamics in strongly interacting 1D Bose gases
- Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain
- Observation of a Majorana zero mode in a topologically protected edge channel
- Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
- Two dimensional anisotropic non Fermi-liquid phase of coupled Luttinger liquids
- Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
- Time-Reversal-Invariant Fractional Josephson Effect
- Intrinsically Gapless Topological Phases
- Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field
- Fractionalized Wave Packets from an Artificial Tomonaga-Luttinger Liquid
- Corner Junction as a Probe of Helical Edge States
- Time-Resolved Observation of Spin-Charge Deconfinement in Fermionic Hubbard Chains
- New quantum phases in a one-dimensional Josephson array
- Direct Observation of Magnon Fractionalization in the Quantum Spin Ladder
- Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator
- Charge-Spin Separation and the Spectral Properties of Luttinger Liquids
- One-Particle an Two-Particle Instability of Coupled Luttinger Liquids
- Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions
- Non-Abelian parafermions in time-reversal invariant interacting helical systems
- Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
- Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
- Field-Controlled Magnetic Order in the Quantum Spin-Ladder System (Hpip)2CuBr4
- Tomonaga-Luttinger Liquid Behavior and Spinon Confinement in YbAlO
- Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
- Novel ordering of an S = 1/2 quasi one-dimensional Ising-like anitiferromagnet in magnetic field
- Direct observation of incommensurate magnetism in Hubbard chains
- Interacting topological edge channels
- Spectral and thermodynamic properties of a strong-leg quantum spin ladder
- Spinons in Conformal Field Theory
- Bound spinons in an antiferromagnetic S=1/2 chain with a staggered field
- Spin correlations in the two-leg antiferromagnetic ladder in a magnetic field
- Atomically Thin Quantum Spin Hall Insulators
- Fermi liquid to Luttinger liquid transition at the edge of a two-dimensional electron gas
- Spin-charge separation in a 1D Fermi gas with tunable interactions
- Spectrum of a magnetized strong-leg quantum spin ladder
- Interacting Bose gases in quasi-one dimensional optical lattices
- Mott Transition for Strongly-Interacting 1D Bosons in a Shallow Periodic Potential
- Attractive Tomonaga-Luttinger Liquid in a Quantum Spin Ladder
- Longitudinal SDW order in a quasi-1D Ising-like quantum antiferromagnet
- Fractional Topological Insulators -- a Pedagogical Review
- 2024 roadmap on 2D topological insulators
- Insulating Josephson-junction chains as pinned Luttinger liquids
- Multiband one-dimensional electronic structure and spectroscopic signature of Tomonoga-Luttinger liquid behavior in KCrAs
- The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
- Wilson ratio of a Tomonaga-Luttinger liquid in a spin-1/2 Heisenberg ladder
- Tunable Fermi-Edge Resonance in an Open Quantum Dot
- Field-induced incommensurate order for the quasi-one-dimensional XXZ model in a magnetic field
- Locallized Magnetism in Low-Dimensional Systems
- Magnetic order and spin fluctuations in low-dimensional insulating systems
- Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas
- SU(2) chiral edge modes of a critical spin liquid
- Helical Liquids in Semiconductors
- Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids
- Bosonization out of equilibrium
- Spinon Confinement and a Sharp Longitudinal Mode in YbPtPb in Magnetic Fields
- Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in Spin Ladders
- Giant magnetic-field dependence of the coupling between spin Tomonaga-Luttinger liquids in BaCo2V2O8
- Vortex lattice melting in a boson-ladder in artificial gauge field
- Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit
- Spin current pumping in helical Luttinger liquids
- A dynamical theory for one-dimensional fermions with strong two-body losses: universal non-Hermitian Zeno physics and spin-charge separation
- Tunable non-equilibrium Luttinger liquid based on counter-propagating edge channels
- Tuning the Many-body Interactions in a Helical Luttinger Liquid
- Low-energy behavior of the spin-tube and spin-orbital models
- Fourier transform of the Luttinger liquid density correlation function with different spin and charge velocities
- Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact
- Finite-temperature perturbation theory for quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets
- Tomonaga-Luttinger Liquid in a Quasi-One-Dimensional S=1 Antiferromagnet Observed by the Specific Heat
- Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas
- Dissipation induced Luttinger liquid correlations in a one dimensional Fermi gas
- Spinon Excitations in the Quasi-1D S = 1/2 Chain Cs4CuSb2Cl12
- Nonlinear spectra of spinons and holons in short GaAs quantum wires
- A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator TaPdTe
- Hierarchy of modes in an interacting system
- The S=1/2 chain in a staggered field: High-energy bound-spinon state and the effects of a discrete lattice
- Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets
- Transport in helical Luttinger liquids in the fractional quantum Hall regime
- Competition between Vortex Unbinding and Tunneling in an Optical Lattice
- Effect of Thermal Fluctuation on Spectral Function for the Tomonaga-Luttinger Model
- Nature of the many-body excitations in a quantum wire: theory and experiment
- Topological transition between competing orders in quantum spin chains
- Direct determination of the Tomonaga-Luttinger parameter in quasi-one-dimensional spin systems
- Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor
- A gate-tunable quantum phase transition in a topological excitonic insulator
- Quasi one-dimensional organic conductors: from Fröhlich conductivity and Peierls insulating state to magnetically-mediated superconductivity, a retrospective
- Thermal disruption of a Luttinger liquid
- Electronic structure of carbon nanotubes on graphene substrates
- Spectral functions of two-band spinless fermion and single-band spin-1/2 fermion models
- Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators
- Theory of Glide Symmetry Protected Helical Edge States in WTe Monolayer
- Bath induced phase transition in a Luttinger liquid
- Splitting of Fermi point of strongly interacting electrons in one dimension: A nonlinear effect of spin-charge separation
- Field-induced antiferromagnetism and Tomonaga-Luttinger liquid behavior in the quasi-one-dimensional Ising-Antiferromagnet SrCo2V2O8
- Characterization of helical Luttinger liquids in microwave stepped-impedance edge resonators
- Spinon continuum in the Heisenberg quantum chain compound SrVO
- Superclimbing modes in transverse quantum fluids: signature statistical and dynamical features
- Instability of sliding Luttinger liquid