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arXiv:1804.02937 · Journal of Physics Condensed Matter

Effective potential and quantum criticality for imbalanced Fermi mixtures

Piotr Zdybel, Paweł Jakubczyk

Published Jun 12, 2018• 9 citations
arXivHTMLPDF

Abstract

We study the analytical structure of the effective action for spin- and mass-imbalanced Fermi mixtures at the onset of the superfluid state. Of our particular focus is the possibility of suppressing the tricritical temperature to zero, so that the transition remains continuous down to T = 0 and the phase diagram hosts a quantum critical point. At mean-field level we analytically identify such a possibility in a regime of parameters in dimensionality d = 3. In contrast, in d = 2 we demonstrate that the occurrence of a quantum critical point is (at the mean-field level) excluded. We show that the Landau expansion of the effective potential remains well-defined in the limit [Formula: see text] except for a subset of model parameters which includes the standard BCS limit. We calculate the mean-field asymptotic shape of the transition line. Employing the functional renormalization group framework we go beyond the mean field theory and demonstrate the stability of the quantum critical point in d = 3 with respect to fluctuations.

DOI
10.1088/1361-648x/aacc00

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We study the analytical structure of the effective action for spin- and mass-imbalanced Fermi mixtures at the onset of the superfluid state. Of our particular focus is the possibility of suppressing the tricritical temperature to zero, so that the transition remains continuous down to T = 0 and the phase diagram hosts a quantum critical point. At mean-field level we analytically identify such a possibility in a regime of parameters in dimensionality d = 3. In contrast, in d = 2 we demonstrate that the occurrence of a quantum critical point is (at the mean-field level) excluded. We show that the Landau expansion of the effective potential remains well-defined in the limit [Formula: see text] except for a subset of model parameters which includes the standard BCS limit. We calculate the mean-field asymptotic shape of the transition line. Employing the functional renormalization group framework we go beyond the mean field theory and demonstrate the stability of the quantum critical point in d = 3 with respect to fluctuations.
We consider a general anisotropic spin-orbit coupling and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS-BEC evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.
We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor $\ensuremath{\approx}$2.722.722.72. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy $|{\ensuremath{\epsilon}}_{B}|$ increases.
We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass imbalances ${m}_{\ensuremath{\downarrow}}/{m}_{\ensuremath{\uparrow}}\ensuremath{\gtrsim}3$. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.
We investigate the phase structure of spin-imbalanced unitary Fermi gases beyond mean-field theory by means of the functional renormalization group. In this approach, quantum and thermal fluctuations are resolved in a systematic manner. The discretization of the effective potential on a grid allows us to accurately account for both first- and second-order phase transitions that are present on the mean-field level. We compute the full phase diagram in the plane of temperature and spin imbalance and discuss the existence of other conjectured phases such as the Sarma phase and a precondensation region. In addition, we explain on a qualitative level how we expect that in situ density images are affected by our findings and which experimental signatures may potentially be used to probe the phase structure.
Fermi gases in strongly coupled regimes are inherently challenging for many-body methods. Although progress has been made analytically, quantitative results require ab initio numerical approaches, such as Monte-Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. For finite spin imbalance, the problem can be circumvented using imaginary polarizations and analytic continuation, and large parts of the phase diagram then become accessible. We propose to apply this strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. We perform a first mean-field analysis which suggests that zero-temperature studies, as well as detecting a potential (tri)critical point, are feasible.
We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy B , whose variation allows one to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance h c , after which there is a first-order phase transition to the normal state. We find that h c , the Chandrasekhar–Clogston limit of superfluidity, has the same value as in three-dimensional systems. We show that for a fixed ratio B / F , where F is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance m c , phase separation is not supported and the normal phase is energetically preferable. The BCS–BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.