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Entanglement spreading after local fermionic excitations in the XXZ chain
by Matthias Gruber, Viktor Eisler
This is not the current version.
|As Contributors:||Viktor Eisler|
|Date submitted:||2020-10-19 10:23|
|Submitted by:||Eisler, Viktor|
|Submitted to:||SciPost Physics|
We study the spreading of entanglement produced by the time evolution of a local fermionic excitation created above the ground state of the XXZ chain. The resulting entropy profiles are investigated via density-matrix renormalization group calculations, and compared to a quasiparticle ansatz. In particular, we assume that the entanglement is dominantly carried by spinon excitations traveling at different velocities, and the entropy profile is reproduced by a probabilistic expression involving the density fraction of the spinons reaching the subsystem. The ansatz works well in the gapless phase for moderate values of the XXZ anisotropy, eventually deteriorating as other types of quasiparticle excitations gain spectral weight. Furthermore, if the initial state is excited by a local Majorana fermion, we observe a nontrivial rescaling of the entropy profiles. This effect is further investigated in a conformal field theory framework, carrying out calculations for the Luttinger liquid theory. Finally, we also consider excitations creating an antiferromagnetic domain wall in the gapped phase of the chain, and find again a modified quasiparticle ansatz with a multiplicative factor.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2020-12-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202010_00016v1, delivered 2020-12-07, doi: 10.21468/SciPost.Report.2262
In the work submitted for publication in SicPost Physics the
authors study the time evolution of the entanglement after
local fermionic excitations are created in a chain described
by the XXZ model. They present numerical results obtained via
density matrix renormalization group, which are initially
analyzed based on a quasiparticle ansatz. To get a better
description of their numerical data, they go further and
present a conformal field theory based calculation. They get
a general good agreement between numerical and analytical
results in the regions of parameters for which both calculations
apply. The manuscript is very well written: assumptions,
calculations, results are all very well explained. I have few
questions and comments that I detail below.
- As in previous works, the authors consider that the spreading
of entanglement is independent of the quasiparticle momentum.
What is the physical justification for this assumption? What
are the implications of it in the results?
- The authors consider that the excitations are created in the
middle of the chain. How do their results and conclusions depend
on this specific choice? In Fig. 1, is the deviation from the
quasiparticle ansatz at zeta ~ 0 related to this choice?
- In both eq. (5) and (13) the authors define the quantity
v_s(q). In eq. (5), the definition applies for the gapless phase,
while eq. (13) holds for the gapped phase. The authors may want
to add a superscript to the quantity to differentiate the two
- In eq. (43), shouldn't V on the left side of the equation depend
on the index j under the product symbol?
Report 1 by Wu-zhong Guo on 2020-12-2 (Invited Report)
- Cite as: Wu-zhong Guo, Report on arXiv:scipost_202010_00016v1, delivered 2020-12-02, doi: 10.21468/SciPost.Report.2249
1. Local excitation for interacting model is interesting
2. The conclusions are supported by both numerical and analytical calculations
1. Some results are vague
2. The physical explanation is not so clear
This paper investigates the dynamical evolution of local
excitation of the XXZ chain model. The authors discuss the evolution of entanglement entropy for different cases including a local fermionic and Majorana excitation. The authors also consider the effect of the strength of interaction. The previous studies on this topic mainly focus on non-interacting models and some simple CFT models. The paper achieves some interesting results by numerical and analytical calculations , thus gives some important insight on the quasiparticle ansatz of local excitation.
I think this paper meets the criteria of acceptance of SciPost. But I have some questions on their results:
1. The results in section 3.2. By tDMRG simulations the authors get some figures (Fig.1) on the variance of $\Delta S$ and $\xi$. They find there exists a peak around $r=0$. This seems very strange. 1). Some points are isolated from others. 2). In section 3.3 the Majorana excitation has no such peaks. I think the authors should explain why the fermionic and Majorana ones are so different. The Majorana is linear combination of two fermionic operators. For me it is more natural that they both show the peaks if the peaks are physical. More, for small strength $\Delta=0.2$ the peaks also appear. But for $\Delta=0$ (free-fermion point) is there a peak by numerical method? In this case the quasiparticle ansatz works well I think there are no peaks.
2. For $|\Delta|\le 1$ (gapless phase) the authors find the maximal $\Delta S$ are associated with coupling $\Delta$ and can be larger than $ln 2$ by numerical calculation shown in Fig.1. But in section 4.1 they find the maximal $\Delta S_2$ is independent with $\Delta $ given by $ln 2$. The authors should explain the tension between the two results.
3. About the results in Fig.5 . Could the authors explain more why the curves oscillate ? Is it from the finite size effect?
4. In the gapless phase the maximal entropy $ln 2$ of the fermionic excitation has a good explanation as EPR-like state. The Majorana excitation is linear combination of two fermionic excitation. It seems the state is given by a linear combination of two EPR-like state thus give the factor 2. If possible the authors could give more physical picture on this results.
see the reports.