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Twisted and untwisted negativity spectrum of free fermions

by Hassan Shapourian, Paola Ruggiero, Shinsei Ryu, Pasquale Calabrese

Submission summary

As Contributors: Paola Ruggiero · Hassan Shapourian
Arxiv Link: https://arxiv.org/abs/1906.04211v1
Date submitted: 2019-06-26
Submitted by: Ruggiero, Paola
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Condensed Matter Physics - Theory

Abstract

A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for fermions that accounts for the Fermi statistics has been put forward. In this paper, we study the many-body spectrum of the reduced density matrix of two adjacent intervals for one-dimensional free fermions after applying the fermionic PT. We show that in general there is a freedom in the definition of such operation which leads to two different definitions of PT: the resulting density matrix is Hermitian in one case, while it becomes pseudo-Hermitian in the other case. Using the path-integral formalism, we analytically compute the leading order term of the moments in both cases and derive the distribution of the corresponding eigenvalues over the complex plane. We further verify our analytical findings by checking them against numerical lattice calculations.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission 1906.04211v1 on 26 June 2019

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