Strongly interacting rotating bosons via complex stochastic - - PowerPoint PPT Presentation

Strongly interacting rotating bosons via complex stochastic quantization

Casey E. Berger and Joaquín E. Drut The University of North Carolina at Chapel Hill

Rotating Bose-Einstein condensates

1949: Onsager predicts rotating superfluids will form vortices

Science 292 5516 (2001)

• Phys. Rev. Lett. 4 14 (1979)

1979: First observation of vortices in rotating 4He 1990s-2000s: rotating BECs in

4He and dilute

atomic gases Advances in theory

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Rotating Bose-Einstein condensates

Theoretical advancements in study of rotating superfluids since 1950s

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Theoretical progress

• Why are we stuck?
• Many-body quantum systems → Quantum Monte Carlo
• Evaluate stochastically, with

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The sign problem

• Action for non-relativistic rotating bosons:
• Complex action
• Usual Quantum Monte Carlo methods do not work
• Proposed solution: Complex Langevin Method

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The Complex Langevin method

• Generalization of stochastic quantization to complex dynamical

variables

• Leads to two coupled SDEs:

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CL: success stories

• Relativistic Bose gas at finite chemical potential
• Lattice action
• Use CL to compute density, field modulus squared

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Aarts, Phys. Rev. Lett (2009)

CL: success stories

• = 0.0

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CL: success stories

• = 0.7

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CL: success stories

• = 1.125

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CL: success stories

• = 1.5

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CL: success stories

Relativistic Bose gas at finite chemical potential

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

µ

1 2 3 4 5 6

Rehˆ ni 44 64 84 104

0.8 0.9 1.0 1.1 1.2 1.3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Aarts, Phys. Rev. Lett (2009)

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CL: success stories

• -h from 0 to 2.0 (bottom to top)
• Dashed lines: 3rd order virial

expansion

• 3+1 dimensional lattice
• Nx = 11, Nt=160

CL results show good agreement with the virial expansion in the virial region

Rammelmüller et al, arxiv: 1807.04664 (2018)

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Density EOS of spin polarized unitary Fermi gas

CL: cautionary tales

• CL is not always successful
• The Excursion Problem
• The probability distribution is not suppressed enough for large values of the

complexified variables

• Causes the imaginary drift term to “run away”
• The Singular Drift Problem
• The probability distribution is not suppressed enough near singularities in the

drift term

• We don’t yet know how to prove when CL will work
• Important to have checks to ensure validity
• Comparisons with existing theoretical benchmarks, experimental

measurements

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Action for our system

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CL in non-relativistic rotating bosons

• Preliminary results for rotating, 2+1D system:
• Average Angular Momentum dependence on rotation frequency
• Nx = 12, NE = 20, E = 0.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0

βωz

0.06 0.04 0.02 0.00 0.02 0.04 0.06

ImhLzi βµ = 4.0 βµ = 3.2 βµ = 2.4 βµ = 1.6 βµ = 0.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0

βωz

0.0 0.2 0.4 0.6 0.8

RehLzi βµ = 4.0 βµ = 3.2 βµ = 2.4 βµ = 1.6 βµ = 0.8 15

CL in non-relativistic rotating bosons

• Preliminary results for rotating, 2+1D system:
• Moment of Inertia dependence on rotation frequency
• Nx = 12, NE = 20, E = 0.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0

βωz

1.5 1.0 0.5 0.0 0.5 1.0

ImhLz/ωzi βµ = 4.0 βµ = 3.2 βµ = 2.4 βµ = 1.6 βµ = 0.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0

βωz

0.0 0.5 1.0 1.5 2.0 2.5 3.0

RehLz/ωzi βµ = 4.0 βµ = 3.2 βµ = 2.4 βµ = 1.6 βµ = 0.8 16

Future directions

• Decrease |01| to study superfluid regime
• Density should show triangular vortex lattice structure
• We expect to see discontinuities in the circulation observable

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Summary and Conclusions

• Many systems of interest inaccessible to QMC due to sign problem
• CL allows us to circumvent the sign problem
• Under some circumstances, CL fails
• Preliminary results for rotating non-relativistic bosons are promising
• More work still to come

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Thank you!

Funding sources:

• Prof. Joaquín Drut

Andrew Loheac Chris Shill Josh McKenney Yaqi Hou

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