Towards overcoming the Monte Carlo sign problem with tensor networks

Abstract

The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.

arXiv comment10 pages, 5 figures; proceedings of XIIth Quark Confinement and the Hadron Spectrum, Thessaloniki 2016

References in corpus (20)

• The density-matrix renormalization group
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• DMRG and periodic boundary conditions: a quantum information perspective
• Matrix product operator representations
• The mass spectrum of the Schwinger model with Matrix Product States
• Optical Abelian Lattice Gauge Theories
• Matrix product states for gauge field theories
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Non-Abelian string breaking phenomena with Matrix Product States
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Chiral condensate in the Schwinger model with Matrix Product Operators
• Hamiltonian simulation of the Schwinger model at finite temperature
• Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Progress in complex Langevin simulations of full QCD at nonzero density
• Two flavor massless Schwinger model on a torus at a finite chemical potential

Cited by in corpus (21)

• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Topological vacuum structure of the Schwinger model with matrix product states
• Real-time simulation of the Schwinger effect with Matrix Product States
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• Tensor network simulation of QED on infinite lattices: learning from (1+1)d, and prospects for (2+1)d
• Path integral contour deformations for noisy observables
• Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks
• Gradient optimization of fermionic projected entangled pair states on directed lattices
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• Loop-Free Tensor Networks for High-Energy Physics
• Discrete-time quantum walks as fermions of lattice gauge theory
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
• A single-particle framework for unitary lattice gauge theory in discrete time
• Meson thermalization with a hot medium in the open Schwinger model