Quantum Monte Carlo simulation of three-dimensional Bose-Fermi mixtures

The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.

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“…In order to circumvent the oscillatory integral(23), we complexify the integration variables 4 x z x y i…”

Section: Path Integral Formulation and The Sign Problemmentioning

confidence: 99%

Lefschetz-thimble analysis of the sign problem in one-site fermion model

2016

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“…We note also that a boson-fermion mixture similar to ours but with up-down fermions was studied for simulating dense QCD matter of strong coupling [35], where the same qualitative result for the T c of BEC was mentioned and a schematic phase diagram is presented for BSC-type fermion pairings as well as the BEC and the density collapse obtained from a semi-classical approximation. A quantum Monte Carlo simulation in three dimensions for a weakly coupled mixture with up-down fermions was also performed in [36] to find that for fixed chemical potentials the BEC (superfluid bosons) is enhanced through the effective chemical potentials with increasing boson-fermion coupling. Our present result gives a more precise many-body description and reason for the phase structure for the weak coupling regime in the absence of the fermion pairings and at given densities of bosons and fermions.…”

Section: Resultsmentioning

confidence: 99%

Bose-Einstein condensation and density collapse in a weakly coupled boson-fermion mixture

2014

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We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation in the weakly coupled boson-fermion many-body mixture of singlecomponent boson and fermion gases, in the case of the repulsive boson-boson and attractive bosonfermion interactions; no fermion-fermion interaction is assumed due to the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the part of bosonic gas in the case where the induced boson-boson attraction mediated by the fermion polarization overcomesthe boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.

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“…Exact diagonalization of the Hamiltonian gives the complete information of physical systems, however it requires an exponentially large amount of the computational cost as the number of particles increases. Monte Carlo simulation of the path integral circumvents this problem, and many physical systems of hadron and condensedmatter physics in thermal equilibrium have been successfully studied with this method [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%