# Entanglement measures and nonequilibrium dynamics of quantum many-body systems: A path integral approach

@article{Ghosh2019EntanglementMA, title={Entanglement measures and nonequilibrium dynamics of quantum many-body systems: A path integral approach}, author={Roopayan Ghosh and Nicolas Dupuis and Arnab Sen and K. Sengupta}, journal={Physical Review B}, year={2019}, volume={101} }

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…

## 2 Citations

### Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

- Physics
- 2020

We present a new method for calculating Renyi entanglement entropies for fermionic field-theories originating from microscopic Hamiltonians. The method builds on an operator identity which we…

### A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons

- Physics
- 2022

A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between…

## References

SHOWING 1-10 OF 56 REFERENCES

### Measuring entanglement entropy in a quantum many-body system

- PhysicsNature
- 2015

Making use of the single-site-resolved control of ultracold bosonic atoms in optical lattices, two identical copies of a many-body state are prepared and interfered to directly measure quantum purity, Rényi entanglement entropy, and mutual information.

### Area laws for the entanglement entropy - a review

- Physics
- 2010

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay…

### Nonequilibrium field theory for dynamics starting from arbitrary athermal initial conditions

- PhysicsPhysical Review B
- 2019

Schwinger Keldysh field theory is a widely used paradigm to study non-equilibrium dynamics of quantum many-body systems starting from a thermal state. We extend this formalism to describe…

### Entanglement entropy and quantum field theory

- Physics
- 2004

We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy SA = −Tr ρAlogρA corresponding to the reduced density matrix…

### Entanglement Entropy across the Superfluid-Insulator Transition: A Signature of Bosonic Criticality.

- PhysicsPhysical review letters
- 2016

The entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model, found that the area-law scaling of entanglements-verified in all the phases-exhibits a sharp singularity at the transition.

### Reduced density matrices and entanglement entropy in free lattice models

- Physics
- 2009

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a…

### Nonequilibrium dynamics of the Bose-Hubbard model: a projection-operator approach.

- PhysicsPhysical review letters
- 2011

A projection-operator formalism is used which allows us to incorporate the effects of quantum fluctuations beyond mean-field approximations in the strong-coupling regime and yields a phase diagram which provides a near exact match with quantum Monte Carlo results in three dimensions.

### Partial time-reversal transformation and entanglement negativity in fermionic systems

- Physics
- 2017

The partial transpose of density matrices in many-body quantum systems, in which one takes the transpose only for a subsystem of the full Hilbert space, has been recognized as a useful tool to…

### Superfluid-insulator transition of two-species bosons with spin-orbit coupling

- Physics
- 2012

Motivated by recent experiments [ Y. J. Lin et al. Nature (London) 471 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a…

### Field Theory of Non-Equilibrium Systems

- Physics
- 2011

The physics of non-equilibrium many-body systems is a rapidly expanding area of theoretical physics. Traditionally employed in laser physics and superconducting kinetics, these techniques have more…