We investigate theoretically a nonrelativistic trace anomaly and its impact on the low-temperature equation of state in spatially one-dimensional three-component fermionic systems with a three-body interaction, which exhibit a nontrivial three-body crossover from a bound trimer gas to dense fermionic matter with increasing density. By applying the G -matrix approach to the three-body interaction, we obtain the analytical expression for the ground-state equation of state relevant to the high-density degenerate regime and thereby address how the three-body contact or, equivalently, the trace anomaly emerges. The analytical results are compared with the recent quantum Monte Carlo data. Our study of the trace anomaly and the sound speed could have some relevance to the physics of hadron-quark crossover in compact stars. Published by the American Physical Society 2024
We investigate theoretically a nonrelativistic trace anomaly and its impact on the low-temperature equation of state in spatially one-dimensional three-component fermionic systems with a three-body interaction, which exhibit a nontrivial three-body crossover from a bound trimer gas to dense fermionic matter with increasing density. By applying the G -matrix approach to the three-body interaction, we obtain the analytical expression for the ground-state equation of state relevant to the high-density degenerate regime and thereby address how the three-body contact or, equivalently, the trace anomaly emerges. The analytical results are compared with the recent quantum Monte Carlo data. Our study of the trace anomaly and the sound speed could have some relevance to the physics of hadron-quark crossover in compact stars. Published by the American Physical Society 2024
We investigate many-body properties of equally populated three-component fermions with attractive threebody contact interaction in one dimension.A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction.We develop a minimal framework that bridges the crossover from tightly bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram.Moreover, we argue that this nontrivial crossover is similar to the hadron-quark crossover proposed in dense matter.A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea.The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.
In ultracold Fermi gases, the spatial dimension and the number of particles involved in interactions largely determine the behavior of the system. By exploiting harmonic trapping potentials and multiple hyperfine states, experiments wield a high degree of control over both of these parameters. In this work, we show that a nonrelativistic, one-dimensional, three-component Fermi system with three-body contact interactions exhibits a quantum anomaly, breaking the scale invariance that exists for this system classically. The exact solution of this three-body problem, wherein a bound trimer forms at arbitrarily small attractive couplings, features a correspondence to the two-dimensional, two-body Fermi system, through which we determine the first non-trivial virial coefficient. We further develop a numerical technique for solving the few-body problem for up to six particles and find that the effective interaction between two trimers is repulsive. To extend our analysis to the many-body problem, we apply the worm algorithm of quantum Monte Carlo and present results for various thermodynamic quantities. We find that for increasing attractive couplings, the system undergoes a Fermi-Fermi crossover from a set of three ideal Fermi gases to one weakly repulsive Fermi gas consisting of massive composite trimers. Finally, we adapt the three-body interaction to a two-dimensional lattice model, where we find strong evidence for a second-order phase transition with an associated reduction in a discrete global symmetry. While the exact experimental parameters we require have not yet been physically realized, our work provides a comprehensive first set of predictions for this model.
A system of three-species fermions in one spatial dimension (1D) with a contact three-body interaction is known to display a scale anomaly. This anomaly is identical to that of a two-dimensional (2D) system of two-species fermions. The exact relation between those two systems, however, is limited to the two-particle sector of the 2D case and the three-particle sector of the 1D case. Here, we implement a nonperturbative Monte Carlo approach, based on the worldline representation, to calculate the thermodynamics and static response of three-species fermions in 1D, thus tackling the many-body sector of the problem. We determine the energy, density, and pressure equations of state and the compressibility and magnetic susceptibility for a wide range of temperatures and coupling strengths. We compare our results with the third-order virial expansion and interpret the classical-quantum crossover as the onset of trimer degrees of freedom.
We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.
In one spatial dimension, quantum systems with an attractive three-body contact interaction exhibit a scale anomaly. In this work, we examine the few-body sector for up to six particles. We study those systems with a self-consistent, nonperturbative, iterative method in the subspace of zero total momentum. Exploiting the structure of the contact interaction, the method reduces the complexity of obtaining the wave function by three powers of the dimension of the Hilbert space. We present results on the energy, momentum, and spatial structure, as well as Tan's contact. We find a Fermi-Fermi crossover interpolating between large, weakly bound trimers and compact, deeply bound trimers: at weak coupling, the behavior is captured by degenerate perturbation theory; at strong coupling, the system is governed by an effective theory of heavy trimers (plus free particles in the case of asymmetric systems). Additionally, we find that there is no trimer-trimer attraction and therefore no six-body bound state.
In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one-dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.