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Journal of Physics Condensed Matter

A continuous line of Berezinskii–Kosterlitz–Thouless phase transition points and the golden ratio point in the three-component fermion ladder

Fei-Jie Huang, Qi-Hui Chen, Yong-Ping Fu, Rong Li Wang

Published Mar 18, 2026• 0 citations
Publisher

Abstract

The realization of the three-component fermion ladder is feasible with current experimental techniques. However, due to complicated interactions among multi-components, theoretical explorations of the system are limited. In this study, we use the bosonization approach to investigate the three-component fermion ladder. We find that the interaction between the third component and the other two alters the system's kinetic structure, giving rise to a continuous line of Berezinskii-Kosterlitz-Thouless transition points in the parameter space and thereby yielding a richer structure of Berezinskii-Kosterlitz-Thouless transitions. We identify a special point, corresponding to the golden ratio under specific approximations, which marks the crossover between weak and strong interaction regimes. This study enhances understanding of the intricate dynamics governing the phase transitions in the three-component fermion ladder and paves the way for future research on one-dimensional multi-component fermion systems.

DOI
10.1088/1361-648x/ae5438

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The realization of the three-component fermion ladder is feasible with current experimental techniques. However, due to complicated interactions among multi-components, theoretical explorations of the system are limited. In this study, we use the bosonization approach to investigate the three-component fermion ladder. We find that the interaction between the third component and the other two alters the system's kinetic structure, giving rise to a continuous line of Berezinskii-Kosterlitz-Thouless transition points in the parameter space and thereby yielding a richer structure of Berezinskii-Kosterlitz-Thouless transitions. We identify a special point, corresponding to the golden ratio under specific approximations, which marks the crossover between weak and strong interaction regimes. This study enhances understanding of the intricate dynamics governing the phase transitions in the three-component fermion ladder and paves the way for future research on one-dimensional multi-component fermion systems.
The equilibrium properties of a weakly interacting atomic Bose gas across the Berezinskii-Kosterlitz-Thouless (BKT) and Bose-Einstein condensation (BEC) phase transitions are numerically investigated through a dimensionality crossover from two to three dimensions. The crossover is realized by confining the gas in an experimentally feasible hybridized trap which provides homogeneity along the planar xyxyxy directions through a box potential in tandem with a harmonic transverse potential along the transverse zzz direction. The dimensionality is modified by varying the frequency of the harmonic trap from tight to loose transverse trapping. Our findings, based on a stochastic (projected) Gross-Pitaevskii equation, showcase a continuous shift in the character of the phase transition from BKT to BEC, and a monotonic increase of the identified critical temperature as a function of dimensionality, with the strongest variation exhibited for small chemical potential values up to approximately twice the transverse confining potential.
Numerical simulations of the full quantum properties of interacting many-body systems by means of field-theoretic Monte Carlo techniques are often limited due to a sign problem. Here we simulate properties of a dilute two-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) transition by means of the complex Langevin (CL) algorithm, thereby extending our previous CL study of the three-dimensional Bose gas to the lower-dimensional case. The purpose of the paper is twofold. On the one hand, it adds to benchmarking of the CL method and thus contributes to further exploring the range of applicability of the method. With the respective results, the universality of the equation of state is recovered, as well as the long-wave-length power-law dependence of the single-particle momentum spectrum below the BKT transition. Analysis of the rotational part of the current density corroborates vortex unbinding in crossing the transition. Beyond these measures of consistency we compute quantum corrections to the critical density and chemical potential in the weakly coupled regime. Our results show a shift of these quantities to lower values as compared to those obtained from classical field theory. It points in the opposite direction as compared to the shift of the critical density found by means of the path-integral Monte Carlo method at larger values of the coupling. Our simulations widen the perspective for precision comparisons with experiment.
We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime are of Berezinskii-Kosterlitz-Thouless type and lie within the same universality class. On the bosonic side of the crossover, our data are well described by the quantum Monte Carlo calculations for a Bose gas. In contrast, in the strongly interacting regime, we observe a superfluid phase which is significantly influenced by the fermionic nature of the constituent particles.
We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wave functions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a nonmonotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition and show that superfluidity is even more sensitive to imbalance than for three-dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allows to identify a phase-separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime.