From Spin Ladders to the 2-d O(3) Model at Non-Zero Density

Abstract

The numerical simulation of various field theories at non-zero chemical potential suffers from severe complex action problems. In particular, QCD at non-zero quark density can presently not be simulated for that reason. A similar complex action problem arises in the 2-d O(3) model -- a toy model for QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The complex action problem of the 2-d O(3) model manifests itself as a sign problem of the ladder system. This sign problem is solved completely with a meron-cluster algorithm.

Based on a talk by U.-J. Wiese, 6 pages, 12 figures, to be published in computer physics communications

References in corpus (1)

• Solution of the Complex Action Problem in the Potts Model for Dense QCD

Cited by in corpus (10)

• D-Theory: Field Quantization by Dimensional Reduction of Discrete Variables
• Study of CP(N-1) θ-Vacua by Cluster-Simulation of SU(N) Quantum Spin Ladders
• From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• Solution to sign problems in models of interacting fermions and quantum spins
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation
• Efficient Cluster Algorithm for CP(N-1) Models
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models