Few-body physics on a space-time lattice in the worldline approach

Abstract

We formulate the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a space-time lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study non-relativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, non-relativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics

arXiv comment18 pages, 14 figures, 5 tables

References in corpus (40)

• Chiral effective field theory and nuclear forces
• Quantum Monte Carlo with Directed Loops
• Quantum Monte Carlo methods for nuclear physics
• Continuous Time Quantum Monte Carlo method for fermions
• Renormalization of the Three-Body System with Short-Range Interactions
• Worm algorithms for classical statistical models
• Lattice simulations for few- and many-body systems
• The Loop Algorithm
• The Complex Langevin method: When can it be trusted?
• Locality and exponential error reduction in numerical lattice gauge theory
• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• Lattice Effective Field Theory for Medium-Mass Nuclei
• The lattice QCD phase diagram in and away from the strong coupling limit
• Properties of nuclei up to $A=16$ using local chiral interactions
• Chiral Limit of Strongly Coupled Lattice Gauge Theories
• Lattice methods for strongly interacting many-body systems
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• Monte Carlo calculations of the finite density Thirring model
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Efficient simulation of relativistic fermions via vertex models
• Phase-diagram of two-color lattice QCD in the chiral limit
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions
• Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions
• Finite-temperature equation of state of polarized fermions at unitarity
• Universal four-component Fermi gas in one dimension
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Pair formation and collapse in imbalanced Fermion populations with unequal masses
• Bosonization and Cluster Updating of Lattice Fermions
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Precision benchmark calculations for four particles at unitarity
• Thermal equation of state of polarized fermions in one dimension via complex chemical potentials
• Benchmark results in the 2D lattice Thirring model with a chemical potential
• Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model
• Lattice theory for nonrelativistic fermions in one spatial dimension
• Transdimensional equivalence of universal constants for Fermi gases at unitarity
• Effective field theory for one-dimensional nonrelativistic particles with contact interaction
• Numerical study of unitary fermions in one spatial dimension
• Finite density condensation and scattering data - a study in ${\varphi }^4$ lattice field theory

Cited by in corpus (5)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• A qubit regularization of the $O(3)$ sigma model
• Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases
• Thermodynamics and static response of anomalous 1D fermions via quantum Monte Carlo in the worldline representation
• Worldline Monte Carlo method for few body nuclear physics