Some experimental tests of Tomonaga-Luttinger liquids

Abstract

The Tomonaga-Luttinger-Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.

Part of the special issue on "Luttinger liquids", Vieri Mastropietro ed

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• Rise and fall of hidden string order of lattice bosons
• Controlling Luttinger liquid physics in spin ladders under a magnetic field
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• Spin-charge separation in two-component Bose-gases
• Field-Controlled Magnetic Order in the Quantum Spin-Ladder System (Hpip)2CuBr4
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Cited by in corpus (18)

• Dipolar physics: A review of experiments with magnetic quantum gases
• Cluster Luttinger Liquids of Rydberg-dressed Atoms in Optical Lattices
• Spreading of correlations in exactly-solvable quantum models with long-range interactions in arbitrary dimensions
• Quantum Critical Dynamics of a Heisenberg-Ising Chain in a Longitudinal Field: Many-Body Strings versus Fractional Excitations
• Circuit Quantum Simulation of a Tomonaga-Luttinger Liquid with an Impurity
• Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
• Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model
• A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta${}_2$Pd${}_3$Te${}_5$
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Magnetic field - temperature phase diagram of ferrimagnetic alternating chains: spin-wave theory from a fully polarized vacuum
• Universality at work -- the local sine-Gordon model, lattice fermions, and quantum circuits
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Anisotropy-induced soliton excitation in magnetized strong-rung spin ladders
• A Luttinger Liquid coupled to Ohmic-class environments
• Spin Correlations in Quantum Wires
• Electron-electron interactions in partially mixed helical states
• Driven Spin-Boson Luttinger Liquids
• One-dimensional extended Hubbard model with soft-core potential