Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach
arXiv:1912.05564 · doi:10.1103/PhysRevB.101.245130
Abstract
We present a path integral formalism for expressing matrix elements of the density matrix of a quantum many-body system between any two coherent states in terms of standard Matsubara action with periodic(anti-periodic) boundary conditions on bosonic(fermionic) fields. We show that this enables us to express several entanglement measures for bosonic/fermionic many-body systems described by a Gaussian action in terms of the Matsubara Green function. We apply this formalism to compute various entanglement measures for the two-dimensional Bose-Hubbard model in the strong-coupling regime, both in the presence and absence of Abelian and non-Abelian synthetic gauge fields, within a strong coupling mean-field theory. In addition, our method provides an alternative formalism for addressing time evolution of quantum-many body systems, with Gaussian actions, driven out of equilibrium without the use of Keldysh technique. We demonstrate this by deriving analytical expressions of the return probability and the counting statistics of several operators for a class of integrable models represented by free Dirac fermions subjected to a periodic drive in terms of the elements of their Floquet Hamiltonians. We provide a detailed comparison of our method with the earlier, related, techniques used for similar computations, discuss the significance of our results, and chart out other systems where our formalism can be used.
arXiv comment23 pages,13 figures, minor changes , version submitted to Phys. Rev. B
References in corpus (49)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Cold bosonic atoms in optical lattices
- Entanglement Entropy and Quantum Field Theory
- Area laws for the entanglement entropy - a review
- Nonequilibrium dynamics of closed interacting quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A spin-orbit coupled Bose-Einstein condensate
- Entanglement entropy and conformal field theory
- Quantum Spin Liquid States
- Synthetic magnetic fields for ultracold neutral atoms
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Measuring entanglement entropy through the interference of quantum many-body twins
- Calculation of reduced density matrices from correlation functions
- Electron Counting Statistics and Coherent States of Electric Current
- On Geometric Entropy
- Reduced density matrices and entanglement entropy in free lattice models
- Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
- Entanglement entropy in free quantum field theory
- A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
- The Mott insulator transition in two dimensions
- Quantum quenches in 1+1 dimensional conformal field theories
- The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
- Strong-coupling expansions for the pure and disordered bose Hubbard model
- Oscillating Superfluidity of Bosons in Optical Lattices
- Phase diagram of the bose Hubbard model
- Entanglement in solvable many-particle models
- Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
- Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
- Partial time-reversal transformation and entanglement negativity in fermionic systems
- Entanglement negativity in the harmonic chain out of equilibrium
- Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
- On the partial transpose of fermionic Gaussian states
- Entanglement spectrum of the two dimensional Bose-Hubbard model
- Full Counting Statistics in the Transverse Field Ising Chain
- Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
- Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations
- Entanglement entropy across the superfluid-insulator transition : a signature of bosonic criticality
- Non-equilibrium dynamics of the Bose-Hubbard model: A projection operator approach
- Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field
- A projection operator approach to the Bose-Hubbard model
- Periodically driven integrable systems with long-range pair potentials
- Superfluid-Insulator transition of two-species bosons with spin-orbit coupling
- Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping
- Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach
- Non-Equilibrium Field Theory for Dynamics Starting from Arbitrary Athermal Initial Conditions
- Full Counting Statistics and Field Theory
- Superfluid-Insulator transition of ultracold atoms in an optical lattice in the presence of a synthetic magnetic field
- Order parameter dynamics of the non-linear sigma model in the large limit
Cited by in corpus (10)
- Analytic approaches to periodically driven closed quantum systems: Methods and Applications
- Entanglement negativity spectrum of random mixed states: A diagrammatic approach
- Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
- Dynamical Transition for a class of integrable models coupled to a bath
- Entanglement Entropy of Free Fermions in Timelike Slices
- Renyi Entropy of Interacting Thermal Bosons in Large Approximation
- Entanglement transitions in a periodically driven non-Hermitian Ising chain
- A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
- Symmetry protected entanglement in random mixed states
- Insights from the exact analytical solution of periodically driven transverse field Ising chain