Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0702191

Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases

X W Guan·M T Batchelor·C Lee·M Bortz
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field $H < H_{c1}$. A completely ferromagnetic phase without pairing occurs when the external field $H > H_{c2}$. In the region $H_{c1} < H < H_{c2}$ we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.

Explore related subjects

cond-mat.str-elcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

X W Guan, M T Batchelor, C Lee, M Bortz. 2007-05-14. Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases. https://doi.org/10.1103/physrevb.76.085120

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Efficient Optimization of Tensor Rings with Low-Rank Environments

Tensor-ring (TR) decompositions provide a natural representation of periodic systems but are difficult to optimize because the closed geometry prevents a global canonical form and leads to costly, ill-conditioned environments. Existing periodic Density Matrix Renormalization Group (DMRG) methods alleviate this difficulty by compressing long environments to a low-rank representation, reducing local operations to $\mathcal{O}(pχ^3)$, where $p$ is the retained environment rank. Here, we extend this approach to an efficient two-site Ring-DMRG algorithm and improve its numerical robustness through appropriate gauge transformations and a generalized Davidson solver. A central challenge in the two-site formulation is the truncation step, which must account for the surrounding environment. When this environment is sufficiently separable, a suitable change of frame reduces the truncation to an ordinary singular value decomposition. When it is not separable, we instead use an alternating optimization that retains the full environment. The computational advantage of tensor rings over tensor trains depends on the scaling of the required environment rank $p$ with bond dimension and system size. For critical systems, the divergent correlation length makes long-range observables remain sensitive to the periodic geometry as the thermodynamic limit is approached. In this regime, the environment rank required to reach a fixed accuracy in the observable does not grow with the system size. Ring-DMRG therefore retains the same cubic scaling with bond dimension as standard DMRG, but at a substantially smaller bond dimension. The low-rank environment construction also provides a systematic generalization of belief propagation (BP), with standard BP recovered in the rank-one limit.

cond-mat.str-el↗
arXiv2026

Lefschetz-Thimble Method to the Sign Problem in the Sachdev-Ye-Kitaev Model

The sign problem in path integrals severely limits the application of quantum Monte Carlo methods to strongly correlated systems, whereas the Lefschetz-thimble method offers a rigorous framework to mitigate this issue. In this paper, we establish a numerical framework based on the Lefschetz thimbles for the Sachdev-Ye-Kitaev (SYK) model. By introducing continuous auxiliary fields via the Hubbard-Stratonovich transformation, the partition function is formulated as a high-dimensional complex integral. We employ the complex Langevin equation to explore the saddle-point distribution of the effective action in the complex plane. Monte Carlo integration is then performed to compute the partition function and Green functions. Our numerical results exhibit excellent agreement with high-temperature expansions, infrared-limit solutions, and determinantal quantum Monte Carlo (DQMC) simulations, confirming the validity of our framework. Furthermore, we demonstrate that our complex Langevin search successfully captures the relevant dominant saddle points governing the SYK model in the large-N limit. Our work deepens the understanding of the sign problem in the SYK model and provides a viable non-perturbative avenue for addressing sign problems in more complex strongly correlated systems.

cond-mat.str-el↗
arXiv2026

Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows

The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.

cond-mat.str-el↗