Renyi Entropy of Interacting Thermal Bosons in Large $N$ Approximation

Abstract

Using a Wigner function based approach, we study the Renyi entropy of a subsystem $A$ of a system of Bosons interacting with a local repulsive potential. The full system is assumed to be in thermal equilibrium at a temperature $T$ and density $\rho$. For a $\mathcal{U}(N)$ symmetric model, we show that the Renyi entropy of the system in the large $N$ limit can be understood in terms of an effective non-interacting system with a spatially varying mean field potential, which has to be determined self consistently. The Renyi entropy is the sum of two terms: (a) Renyi entropy of this effective system and (b) the difference in thermal free energy between the effective system and the original translation invariant system, scaled by $T$. We determine the self consistent equation for this effective potential within a saddle point approximation. We use this formalism to look at one and two dimensional Bose gases on a lattice. In both cases, the potential profile is that of a square well, taking one value in the subsystem $A$ and a different value outside it. The potential varies in space near the boundary of the subsystem $A$ on the scale of density-density correlation length. The effect of interaction on the entanglement entropy density is determined by the ratio of the potential barrier to the temperature and peaks at an intermediate temperature, while the high and low temperature regimes are dominated by the non-interacting answer.

arXiv comment12 pages, 4 figures

References in corpus (34)

• Quantum entanglement
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• A bound on chaos
• Detecting topological order in a ground state wave function
• Aspects of Holographic Entanglement Entropy
• Many-body localization, thermalization, and entanglement
• Entanglement entropy and conformal field theory
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Calculation of reduced density matrices from correlation functions
• On the role of entanglement in quantum computational speed-up
• Identifying Topological Order by Entanglement Entropy
• Many-body localization: an introduction and selected topics
• Entanglement entropy in free quantum field theory
• Quantum Field Theory in the Large N Limit: a review
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Keldysh technique and non-linear sigma-model: basic principles and applications
• Entanglement Entropy in the O(N) model
• Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
• Entanglement and boundary critical phenomena
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Universal geometric entanglement close to quantum phase transitions
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Conformal Field Theory on the Fermi Surface
• Non-Equilibrium Field Theory for Dynamics Starting from Arbitrary Athermal Initial Conditions
• Power-law entanglement growth from typical product states
• Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach
• Extremal statistics of entanglement eigenvalues can track the many-body localized to ergodic transition
• Entanglement of Free Fermions and Bosons at Finite Temperature

Cited by in corpus (4)

• Non-equilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems
• Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
• Entanglement in the full state vector of boson sampling
• Building Entanglement Entropy out of Correlation Functions for Interacting Fermions