Getting Around the Sign Problem to Solve an Open Quantum System
© The Physical Society of Japan
This article is on
Lattice Lindblad simulation
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2022, 053B03 (2022).
Researchers from Japan have found a novel nonequilibrium quantum system that doesn’t have the sign problem. The transport properties of the system are simulated with a Monte Carlo approach.
Quantum computing and superconductivity are prospective disruptive technological advancements capable of deeply impacting our society. Our understanding of these properties depends on our understanding of complex quantum matter systems, a first step towards which involves understanding the exotic topological properties directly intertwined with the lattice of solid quantum systems through simulation.
The sign problem is one of the major unsolved problems in the physics of manyparticle systems and is present when calculating the properties of a quantum mechanical system described by many strongly interacting fermions or in field theories of a nonzero strongly interacting fermion density. As the fermionic particles are strongly interacting, analytical methods are not applicable, and neither is perturbation theory, a popular mathematical tool. The only option is to use bruteforce numerical methods, such as Monte Carlo sampling.
Because the particles are fermions, the interchange of any two particles leads to a change of sign in the wavefunction. The net quantummechanical sum over all multiparticle states is then achieved by an integral over a function that is highly oscillatory. Such an integral is hard to evaluate numerically and can be a source of significant error. The error in evaluating the system grows with the number of particles, so, the sign problem is extreme within the thermodynamic limit, unless there are cancellations arising from some symmetry of the system.
In a new study, researchers have examined a novel exceptional case of open quantum systems—a nonrelativistic spinless fermion with dissipative dynamics. The lattice formulation of the system is based on the famous SchwingerKeldysh path integral representation. Through the theoretical framework of the path integral representation of the Lindblad equation, the particularity of the dissipative term leads to an exact quenching of the fermion determinant. The researchers obtained a fermion determinant that is positive definite, meaning that the sign problem is not present in the Monte Carlo simulation.
Although an electric current operator was used in this case, the researchers suggest quenching can be achieved for any bilinear Hermitian jump operator. This work allows the use of realtime lattice simulation to investigate charge transport in a nonequilibrium freefermion theory governed systems, providing a new handy tool to the quantum mechanics’ toolbox.
Bilinear and Hermitian jump operators can only exactly describe trivial steady states, however. For the study of the formation of other nonequilibrium steady states, different example models without the sign problem need to be uncovered. This work plots a course for future discoveries, wherein circumventing the sign problem could help guide our understanding of quantum matter and its properties.
Lattice Lindblad simulation
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2022, 053B03 (2022).
Share this topic
Fields
Related Articles

Understanding NonInvertible Symmetries in Higher Dimensions Using Topological Defects
Theoretical Particle Physics
2024927
By constructing KramersWannierWegner duality and Z_{2} duality defects and deriving their crossing relations, this study presents the first examples of codimension one noninvertible symmetries in fourdimensional quantum field theories.

Quantum Mechanics of OneDimensional ThreeBody Contact Interactions
Mathematical methods, classical and quantum physics, relativity, gravitation, numerical simulation, computational modeling
Theoretical Particle Physics
2024213
The quantum mechanical description of topologically nontrivial threebody contact interactions in one dimension is not well understood. This study explores the Hamiltonian description of these interactions using the pathintegral formalism.

Investigating Unitarity Violation of Lee–Wick’s Complex Ghost with Quantum Field Theory
Theoretical Particle Physics
2024119
Theories with fourthorder derivatives like Lee–Wick’s quantum electrodynamics model or quadratic gravity result in complex ghosts above a definite energy threshold that violate unitarity.

Investigating Δ and Ω Baryons as Meson–Baryon Bound States in Lattice Quantum Chromodynamics
Theoretical Particle Physics
2023713
We investigate Δ and Ω baryons as meson–baryon bound states in lattice quantum chromodynamics and show that their difference results from the kinematic structure of the two meson–baryon systems, and not their interaction.

Novel Insights Into Bulk Reconstruction in the Antide Sitter/Conformal Field Theory Correspondence
Theoretical Particle Physics
202361
Bulk reconstruction in antide Sitter/conformal field theory is fundamental to our understanding of quantum gravity. We show that contrary to popular belief, bulk reconstruction is rather simple and intuitive.