Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
arXiv:2001.10486 · doi:10.1140/epjc/s10052-020-08493-8
Abstract
In this paper, by analyzing the underlying Lefschetz thimble structure, we study quantum phases in zero-dimensional scalar field theories with complex actions. Using first principles, we derive the Lefschetz thimble equations of these models, and discuss the issues when we apply the same calculations for more complicated systems. We also derive the conditional expressions involving relations among the parameters of the model, that would help us predict quantum phase transitions in these systems.
arXiv commentv3: 35 pages, 11 figures. References updated. Published version
References in corpus (60)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Complex Extension of Quantum Mechanics
- Introduction to PT-Symmetric Quantum Theory
- High density QCD on a Lefschetz thimble?
- Analytic Continuation of Liouville Theory
- Analytic Continuation Of Chern-Simons Theory
- Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
- Complex Langevin: Etiology and Diagnostics of its Main Problem
- A Primer on Resurgent Transseries and Their Asymptotics
- An Introduction to Resurgence, Trans-Series and Alien Calculus
- Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
- Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
- Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
- Controlling complex Langevin dynamics at finite density
- Resurgence theory, ghost-instantons, and analytic continuation of path integrals
- Solution of Schwinger-Dyson Equations for -Symmetric Quantum Field Theory
- A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
- New insights into the problem with a singular drift term in the complex Langevin method
- Monte Carlo study of real time dynamics
- Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
- Structure of Lefschetz thimbles in simple fermionic systems
- Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
- Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
- An efficient method to compute the residual phase on a Lefschetz thimble
- Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
- Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
- Stability of complex Langevin dynamics in effective models
- Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
- Deep Learning Beyond Lefschetz Thimbles
- Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
- Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
- Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model
- Localised distributions and criteria for correctness in complex Langevin dynamics
- Monte Carlo calculations of the finite density Thirring model
- Tempered transitions between thimbles
- Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
- Lefschetz-thimble techniques for path integral of zero-dimensional sigma models
- Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
- Functional methods for false vacuum decay in real time
- One-dimensional QCD in thimble regularization
- A New Look At The Path Integral Of Quantum Mechanics
- Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
- Complex saddle points in QCD at finite temperature and density
- Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
- Finite Density Near Lefschetz Thimbles
- Fisher's zeros as boundary of renormalization group flows in complex coupling spaces
- Complexified Path Integrals and the Phases of Quantum Field Theory
- Combining the complex Langevin method and the generalized Lefschetz-thimble method
- Resurgence and Holomorphy: From Weak to Strong Coupling
- The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
- Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
- A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
- Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
- Formulation of Complex Action Theory
- Complex Langevin Dynamics in Large Unitary Matrix Models
- Path integration and perturbation theory with complex Euclidean actions
- Taming the sign problem of the finite density Hubbard model via Lefschetz thimbles
- Temporal breakdown and Borel resummation in the complex Langevin method
- Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region