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Researchers demonstrate attractive interactions in a Tomonaga-Luttinger liquid

Understanding quantum many body phenomena is a fundamental challenge to modern science, and remains a formidable task in most cases. However, when interacting quantum particles, either bosons or fermions, are confined to one dimension, certain universal features emerge such that a detailed effective description becomes available. This canonical phase, with peculiar properties like algebraic correlations and fractionalized excitations, is called the Tomonaga-Luttinger liquid (TLL).
All known physical realizations of TLLs, ranging from carbon nanotubes to semiconductor nanowires, support repulsive interactions, while the theory puts both repulsive and attractive interactions on an equal footing. By measurements in a magnetic insulator, the researchers at LNCMI Grenoble demonstrate the first realization of a TLL with attractive interactions.
They made use of a high quality crystal of (C7H10N)2CuBr4 (DIMPY) grown by an ETH Zürich team, which features a ladder-like magnetic network of Cu2+ ions (S=1/2) with Heisenberg antiferromagnetic exchanges. Such a quantum spin ladder can be described as a TLL of interacting spinless fermions when a sufficiently strong magnetic field is applied. Whether the interactions are repulsive or attractive depends on the ratio of the magnetic exchange strength along the leg and the rung, i.e. a strong-leg ladder as DIMPY supports attractive interactions while a strong-rung ladder the repulsive interactions.
The DIMPY crystal was cooled below 1 K using a dilution refrigerator to enter a quantum regime, and placed under a magnetic field up to 15 T provided by a superconducting magnet of high homogeneity. The Grenoble team employed a nuclear magnetic resonance (NMR) to probe excitations in the low energy limit, through the NMR relaxation rate (1/T1) measurements.
From the 1/T1 measurements as a function of temperature in various magnetic fields, they confirmed a power-law decay of correlation functions, and the field-dependent variation of the power-law exponents which reflects the sign and strength of the interaction. By comparing the experimental data with the theoretical expression, they concluded that the interactions between the spinless fermions are indeed attractive and the interaction strength is field dependent. Moreover, they confirmed that the system approaches a noninteracting regime when the field is tuned toward a critical value, as predicted.
These results allow an invaluable comparative study of the TLLs with repulsive and attractive interactions, e.g. how they lead to different behaviour, with the capability of controlling the interaction strength by the applied magnetic field.
Figure: (left) Crystal structure of DIMPY showing a ladder-like magnetic network of Cu (S=1/2) ions. (right) Typical NMR relaxation rate 1/T1 as a function of temperature, measured in 15 T, where the slope corresponds to attractive interactions between the spinless fermions.
Contact:  Mingee CHUNG - Mladen HORVATIC
M. Jeong, H. Mayaffre, C. Berthier, D. Schmidiger, A. Zheludev, and M. Horvatic,” Attractive Tomonaga-Luttinger Liquid in a Quantum Spin Ladder,” Phys. Rev. Lett. 111, 106404 (2013).