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arXiv:2602.17656 · Physical Review Letters

Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas

Alvise Bastianello, Yi Zeng, Sudipta Dhar, Zekui Wang, Xudong Yu, Milena Horvath, Grigori E. Astrakharchik, Yanliang Guo, Hanns-Christoph Nägerl, Manuele Landini

cond-mat.quant-gascond-mat.stat-mechquant-phSubmitted Feb 19, 2026• Announced Feb 20, 2026• 1 citation

v1 · Feb 19, 2026 v2 · Jun 10, 2026

Abstract

Critical quantum field theories occupy a central position in modern theoretical physics for their inherent universality stemming from long-range correlations. As an example, the Tomonaga-Luttinger liquid (TLL) describes a wealth of one-dimensional quantum systems at low temperatures. Its behavior is deeply rooted in the emergence of an effective Fermi sea, leading to power-law correlations and Friedel oscillations. A promising direction to realize systems exhibiting novel universal behavior beyond TLL is through the generalization of the underlying Fermi sea. In this Letter, we show that fractional Fermi seas with reduced occupancy arise in an integrable Bose gas driven out of equilibrium by cyclic changes in interactions from repulsive to attractive. The correlation functions feature signatures of criticality incompatible with a conventional TLL, suggesting a novel critical phase. Our predictions, based on Generalized Hydrodynamics, are directly relevant to cold atoms.

Journal reference: Phys. Rev. Lett. 136, 230402 (2026)
DOI: 10.1103/j3s5-gjpf

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Critical quantum field theories occupy a central position in modern theoretical physics for their inherent universality stemming from long-range correlations. As an example, the Tomonaga-Luttinger liquid (TLL) describes a wealth of one-dimensional quantum systems at low temperatures. Its behavior is deeply rooted in the emergence of an effective Fermi sea, leading to power-law correlations and Friedel oscillations. A promising direction to realize systems exhibiting novel universal behavior beyond TLL is through the generalization of the underlying Fermi sea. In this Letter, we show that fractional Fermi seas with reduced occupancy arise in an integrable Bose gas driven out of equilibrium by cyclic changes in interactions from repulsive to attractive. The correlation functions feature signatures of criticality incompatible with a conventional TLL, suggesting a novel critical phase. Our predictions, based on Generalized Hydrodynamics, are directly relevant to cold atoms.

The one-dimensional (1D) Yang-Gaudin model--an integrable

δ

-function interacting Fermi gas, serves as a paradigm in quantum many-body physics, encompassing phenomena from spin-charge separation to the Luther-Emery liquid. However, a consistent description of the Luther-Emery liquid and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like pairing states in the 1D attractive Fermi gas remains elusive. In this work, we develop a universal Tomonaga-Luttinger liquid (TLL) theory to describe the FFLO state both for the case of weak and strong binding between fermions of opposite spins. We rigorously derive a low-energy effective Hamiltonian using bosonization, revealing the emergence of a two-component TLL: one exhibiting spin-charge coupling in the weak binding regime, and another featuring charge-charge separation in the strong binding regime. For the weak binding regime, we further derive renormalization-group equations for the sine-Gordon term in the spin sector and show that this term undergoes a relevant-irrelevant phase transition driven by the magnetic field. We further analyze the dynamical correlation functions of the FFLO pairing state based on the effective Hamiltonian we constructed. Finally, we discuss experiments using ultracold atoms to elucidate the Luther-Emery liquid behavior and the subtle phenomena of spin-charge coupling and charge-charge separation.

We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.

The Pauli exclusion principle is a cornerstone of quantum physics: it governs the structure of matter. Extensions of this principle, such as Haldane's generalized exclusion statistics, predict the existence of exotic quantum states characterized by fractional Fermi seas (FFS), i.e. momentum distributions with uniform but fractional occupancies. Here, we report the experimental realization of fractional Fermi seas in an excited one-dimensional Bose gas prepared through ramping cycles in the interaction strength. The resulting excited yet stable Bose-gas states exhibit Friedel oscillations, smoking-gun signatures of the underlying FFS. The stabilization of these states offers an opportunity to deepen our understanding of quantum thermodynamics in the presence of exotic statistics and paves the way for applications in quantum information and sensing.

The Pauli exclusion principle is a cornerstone of quantum physics: it governs the structure of matter. Extensions of this principle, such as Haldane's generalized exclusion statistics, predict the existence of exotic quantum states characterized by fractional Fermi seas (FFS), i.e. momentum distributions with uniform but fractional occupancies. Here, we report the experimental realization of fractional Fermi seas in an excited one-dimensional Bose gas prepared through ramping cycles in the interaction strength. The resulting excited yet stable Bose-gas states exhibit Friedel oscillations, smoking-gun signatures of the underlying FFS. The stabilization of these states offers an opportunity to deepen our understanding of quantum thermodynamics in the presence of exotic statistics and paves the way for applications in quantum information and sensing.

We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|(β), with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a "Luttinger staircase." Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multicomponent strongly attractive fermionic atoms with enlarged SU

(N)

spin symmetry and Zeeman splitting. Universal multicomponent Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral

N

-atom composites and spin-$(N\ensuremath{-}1)/2$ single atoms. The equation of state which we obtained provides a precise description of multicomponent composite fermions and opens up the study of quantum criticality in one-dimensional systems of

δ

-component Fermi gases with population imbalance.