Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

Loheac, Andrew C.; Braun, Jens; Drut, Joaquín E.; Roscher, Dietrich

doi:10.1103/physreva.92.063609

Cited by 19 publications

(36 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Still, mean field results suggest that interesting features of the phase diagram lie within the region where extrapolation works [9]. For the one dimensional case, this avenue has been tested numerically [10]. Another approach is the Complex Langevin method where the configuration space is augmented by complexifying the field variables and stochastic process is used to sample configurations in this complex space [11,12].…”

Section: Introductionmentioning

confidence: 99%

Spin polarized nonrelativistic fermions in 1+1 dimensions

2018

View full text Add to dashboard Cite

We study by Monte Carlo methods the thermodynamics of a spin polarized gas of non-relativistic fermions in 1+1 dimensions. The main result of this work is that our action suffers no significant sign problem for any spin polarization in the region relevant for dilute degenerate fermi gases. This lack of sign problem allows us to study attractive spin polarized fermions non-perturbatively at spin polarizations not previously explored. For some parameters values we verify results previously obtained by methods which include an uncontrolled step like complex Langevin and/or analytical continuation from imaginary chemical potential. For others, larger values of the polarization, we deviate from these previous results.

show abstract

Section: Introductionmentioning

confidence: 99%

Spin polarized nonrelativistic fermions in 1+1 dimensions

2018

View full text Add to dashboard Cite

show abstract

“…However, a complete derivation of the thermodynamics of an arbitrarily polarized gas and the role of pair fluctuation in 1D systems still remain a challenging problem in the field of cold atoms [25,30,35,36].…”

mentioning

confidence: 99%

Universal properties of Fermi gases in one dimension

He¹,

Chen²,

Zhang³

et al. 2016

Phys. Rev. A

View full text Add to dashboard Cite

In this Rapid Communication, we investigate the universal properties of a spin-polarized twocomponent Fermi gas in one dimension (1D) using Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility and the contact susceptibility, giving a precise understanding of the 1D analogue of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimension (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility χ ∼ 1/ √ T exp(−∆/T ) at low temperatures, where ∆ is the energy gap and T is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization P and the contact C for both repulsive and attractive Fermi gases. Our findings emphasize the role of the pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions. In the past decade, remarkable progresses have been made in the study of strongly interacting fermions in three-dimensional (3D) Bose-Einstein condensate(BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover [1-4], including precise measurements of equations of states (EOS) [5][6][7][8], the investigations of magnetic and pairing/depairing phenomena [9][10][11] and polaron [12][13][14][15] in a spin polarized system. In addition, the 2D Fermi gas has also been realized and attracted a lot of attention both experimentally [16][17][18][19][20][21][22][23] and theoretically [24][25][26][27][28]. Despite these advances, fundamental questions still remain. In particular, what is the role of pair fluctuations on thermodynamics and transport phenomena, especially in the vicinity of transition temperature at unitarity.Similar questions can be answered in a more affirmative manner in the case of 1D Fermi gases due to the existence of exactly solvable models. Recently, dramatical progresses have been made in the experimental realizations of many exactly solvable models of 1D interacting bosons and fermions [29,30]. One naturally expects to gain deeper insight into the 1D analogue of the 3D BEC-BCS crossover as well as the associated universal thermodynamics from the Bethe ansatz perspective. In fact, the precise equation of state obtained from the thermodynamic Bethe ansatz (TBA) equations [31] not only gives rise to important characteristics of the Tomonaga-Luttinger liquids (TLL) but also * The authors WBH and YYC contributed equally to the calculations in this paper.provides universal laws, such as quantum scalings, dimensionless ratios, Tan's contact and universal relations between macroscopic properties [32][33][34], which could shed new light on many-body phenomena in higher dimensions. However, a complete derivation of the thermodynamics of an arbitrarily polarized gas and the role of pair fluctuation in 1D systems still remain a challenging problem in the field of cold atoms [25,30,35,36].In this Rapid Communication, we show that the TBA equati...

show abstract

“…Such an analytic continuation appears to become increasingly unreliable for large imbalances; see Ref. [14] and also Refs. [11,15] where this has also been observed in the case of imaginary mass imbalances.…”

Section: Polarized Systemmentioning

confidence: 99%

“…[13] and first applied to the system studied here in Ref. [14]. For a variety of dimensionless chemical potential asymmetries βh, the normalized total density n/n 0 = (n ↑ +n ↓ )/n 0 obtained from this approach is displayed in Fig.…”

Section: Polarized Systemmentioning

confidence: 99%

Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

Loheac¹,

Braun

Drut

2018

EPJ Web Conf.

Self Cite

View full text Add to dashboard Cite

Abstract. We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick's theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.

show abstract

Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

Cited by 19 publications

References 76 publications

Spin polarized nonrelativistic fermions in 1+1 dimensions

Spin polarized nonrelativistic fermions in 1+1 dimensions

Universal properties of Fermi gases in one dimension

Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

Contact Info

Product

Resources

About