A duality principle for the multi-block entanglement entropy of free fermion systems

Abstract

The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set $A$ of sites of the subsystem considered and the set $K$ of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets $A$ and $K$ to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets $A$ and $K$ consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and $r$-partite information generalizing the known ones for the single block case.

12 pages, 5 figures, typeset in LaTeX

References in corpus (11)

• Entanglement entropy of two disjoint intervals in conformal field theory II
• Remarks on the entanglement entropy for disconnected regions
• Entanglement of low-energy excitations in Conformal Field Theory
• Entanglement entropy of two disjoint blocks in XY chains
• The entanglement entropy of one-dimensional gases
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Excited state entanglement in homogeneous fermionic chains
• Entanglement in the XX spin chain with an energy current
• Entanglement of several blocks in fermionic chains
• Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions
• Supersymmetric spin chains with non-monotonic dispersion relation: criticality and entanglement entropy

Cited by in corpus (13)

• Free-Fermion entanglement and orthogonal polynomials
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Entanglement of magnon excitations in spin chains
• Inhomogeneous XX spin chains and quasi-exactly solvable models
• Entanglement of Free Fermions on Johnson Graphs
• Entanglement Entropy of Fermions from Wigner Functions: Excited States and Open Quantum Systems
• Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions
• Entanglement of Free Fermions on Hadamard Graphs
• Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
• Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• Volume-law entanglement fragmentation of quasiparticles