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Entanglement links and the quasiparticle picture
[article]

2022
*
arXiv
*
pre-print

*N*−a. ... 1 + 1 2(1 −

*n*) ∂ z T

*n*(z), (6) where T

*n*(z) is the twist field operator of order

*n*[10-12], and we define J R (z) as the equivalent anti-holomorphic part. ...

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Symmetry protected phases in inhomogeneous spin chains
[article]

2018
*
arXiv
*
pre-print

L−

arXiv:1812.04869v1
fatcat:knvzr32kxnesbcwaslmihl6mbm
*n*| H |• L−*n*• L−*n*| H 0 (*n*−1) • L−*n*| H |• L+*n*0 (*n*−1) H |• L−*n*0 (*n*−1) H 0 (*n*−1) 0 (*n*−1) H |• L+*n*• L+*n*| H |• L−*n*• L+*n*| H 0 (*n*−1) • L+*n*| H |• L+*n* *n*= 1, ..., L − 1 (20) The last step of the ...*n*+1 + S −*n*S +*n*+1 + ∆ 2 S z*n*S z*n*+1 ≡ 2L*n*=1 J*n*(S*n*· S*n*+1 ) ∆ ≡ 2L*n*=1 h*n*, (32) where J*n*follow the rule expressed in Eq. (3). ...##
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Entanglement in non-critical inhomogeneous quantum chains
[article]

2021
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arXiv
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pre-print

Using Eq. (4) we have ∂ t α

arXiv:2107.12113v1
fatcat:h6fxjcdfcfakfczqqpdbb45d2u
*n*= −2e −2h*n*β*n*− e sign(*n*)h β*n*−1 ∂ t β*n*= 2e −2h*n*α*n*− e sign(*n*)h α*n*+1 . (21) Now, we define the fields α m = √ aα(x), β m = √ aβ(x), (22) where a is the lattice spacing ... Covariance matrices of states*n*= 4⟩ and*n*= 5⟩ for h = 10 and*N*= 20. ... Considering 1 <*n*< L − 2 central decimations, the overlapping ⟨*n*= 2m*n*= 0⟩ with m = 0, ⋯, L − 1 decreases the total number of loops to*N*− m while the overlapping ⟨*n*= 2m − 1*n*= 0⟩ with m = 1, ⋯, L ...##
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Casimir forces on deformed fermionic chains

2021
*
Physical Review Research
*

Rodríguez-López,

doi:10.1103/physrevresearch.3.013062
fatcat:clnzzk57tvct3ftfgcufqfkosi
*N*. Samos Sáenz de Buruaga, and G. Sierra for very useful discussions. Also, we acknowledge the Spanish government for financial support through Grants No. ... varying hopping amplitudes, we obtain F*N*≡ −c 0 − c B 2 J*N*J*N*− π 12*N*2 + π S*N*6J*N**N*3 . ( 28 ) Let us consider the terms individually. ... For very weak deformations (J*N*≈ J 0 + δJ*N*is a small deformation), we can assume that S*N*≈ NJ*N*, and we obtain F*N*≈ −c 0 − c B 2 J*N*J*N*+ π 12*N*2 . ( 29 ) Thus we are led to the following claim: ...##
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Power Accretion in Social Systems
[article]

2019
*
arXiv
*
pre-print

Assuming that the effective number of agents is

arXiv:1902.03288v1
fatcat:yrsg272fhfbgtdev5wzsm7iztq
*N*eff ∼ exp(S), exp(S)/*N*=*N*eff /*N*, i.e. the fraction of high class agents, which for long times converge to ≈ 1/3. ... Moreover, we will define the Lorenz curve [26] , L(k/*N*) is the total power possessed by the poorest k players: L(k/*N*) = k i=1 ω*N*−i+1 . (6) The Lorenz curve allows to define the Gini coefficient [ ...##
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Entanglement as geometry and flow
[article]

2019
*
arXiv
*
pre-print

We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all 2^

arXiv:1906.05146v1
fatcat:t5y2tcjrerc2tnq3v4eokbxhue
*N*bipartitions of an*N*-party pure quantum system by means ... J(x) = lim*n*→1 1 2(1 −*n*) ∂ x T*n*(x) , (32) and the same expression withT*n*(x). ... For the interval A = (u, v) in the infinite line one has tr A ρ*n*A = T*n*(u)T*n*(v) = c*n*((v − u)/ε)) 2∆*n*, (30) where T*n*(x), and its conjugateT*n*(x), are twist fields with the same scaling dimension ...##
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Depletion in fermionic chains with inhomogeneous hoppings
[article]

2022
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arXiv
*
pre-print

Then, J

arXiv:2209.10624v1
fatcat:v3za64ssvnb3plpryyu4tmhs4q
*n*−1 ψ*n*−1 + J*n*ψ*n*+1 = Eψ*n*, (42) which can be rewritten for very smooth J as J*n*(ψ*n*−1 + ψ*n*+1 ) ≈ Eψ*n*. (43) Now we can take the hopping amplitude to the RHS, assuming that it is non-zero ... , ψ*n*−1 + ψ*n*+1 − E J*n*− E ψ*n*≈ Eψ*n*, (44) which can be read as a homogeneous hopping Hamiltonian with a chemical potential µ*n*of the form µ*n*= E 1 J*n*− 1 , (45)*n*i i ν = 1/2 ν = 3/8 ν = ν = 1/8 ...##
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Entanglement as geometry and flow

2020
*
Physical review B
*

We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all 2

doi:10.1103/physrevb.101.195134
fatcat:gcpi7bbdjvfdvlyi46jxd6f2va
*N*bipartitions of an*N*-party pure quantum system by means ... defining S (*n*) A and J (*n*) i j . ...*n*= c 12 (*n*− 1/*n*), and c*n*is a nonuniversal constant whose value at*n*= 1 is c 1 = 1 to guarantee the normalization condition tr A ρ A = 1. ...##
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Nanowire reconstruction under external magnetic fields
[article]

2020
*
arXiv
*
pre-print

We can write now: Z = {xi} V x1 T x1,x2 V x2 T x2,x3 V x3 · · · T x

arXiv:1910.04129v2
fatcat:i5h34pf4wrgijhahb7edzntyqm
*N*−1 ,x*N*V x*N*= {xi} V x1 M x1,x2 M x2,x3 · · · M x*N*−1 ,x*N*= x1,x*N*V x1 (M )*N*−1 x1,x*N*= V T (M )*N*−1 S, (6) where S = (1, · ... Then, r i = 1 Z {xi} V x1 M x1,x2 · · · R xi M xi,xi+1 · · · M x*N*−1 ,x*N*s i = 1 Z {xi} V x1 M x1,x2 · · · S xi M xi,xi+1 · · · M x*N*−1 ,x*N*. (8) Two-point correlators are found in a similar way, inserting ...##
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Ergotropy and entanglement in critical spin chains
[article]

2022
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arXiv
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pre-print

Sierra and

arXiv:2207.13998v1
fatcat:s66sh43ypvdpha6jwdhsvuco6e
*N*. Samos Sáenz de Buruaga. This work was funded by the Spanish government through grants PGC2018-094763-B-I00 and PID2019-105182GB-I00. ... 0 2 − π 24(*N*+ 1) 2 + (−1)*n*2(*N*+ 1) sin π(*n*+1/2)*N*+1 , (28 ) which, since*N*/2 is even, reduces for the central link to C*N*/2,*N*/2+1 ≈ − c 0 2 − π 24(*N*+ 1) 2 + 1 2(*N*+ 1) , (29) yielding E A ≈ −c 0*N*... Q A •*N*log 2*N*∆E A ≈ α 1 − α 2*N*, W A ≈ α 1 − α 2*N*− α 3 log 2 (α 4*N*)*N*, Q A ≈ α 3 log 2 (α 4*N*)*N*. (42) In our case the optimal values of the parameters are α 1 ≈ 0.137, α 2 ≈ 0.07, α 3 ≈ 0.044 ...##
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Casimir forces on deformed fermionic chains
[article]

2020
*
arXiv
*
pre-print

Rodríguez-López,

arXiv:2004.12456v2
fatcat:clsgzlza5nggxpurc5h33nq2im
*N*. Samos Sáenz de Buruaga and G. Sierra for very useful discussions. ... J*N*J*N*− π 12*N*2 + πS*N*6J*N**N*3 , (11) Let us consider the terms individually. ... For very weak deformations, J*N*≈ J 0 + δJ*N*is a small deformation, we can assume that S*N*≈*N*J*N*, so we obtain F*N*≈ −c 0 − B 2 J*N*J*N*+ π 12*N*2 . (12) The validity of expression (12) can be checked ...##
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Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
[article]

2019
*
arXiv
*
pre-print

c †

arXiv:1912.10788v1
fatcat:jingtiji5zginmgkzpf7q3npmy
*N*ψ i ⟩⟨ψ i c*N*ψ 0 ⟩ ki − ∑*N*i=1 ⟨ψ 0 c †*N*ψ i ⟩⟨ψ i c*N*ψ 0 ⟩ ki ⎞ ⎠ + J l J r ⎛ ⎝ ⟨l, r c † l c r l ′ , r ′ ⟩ ∑*N*i=1 ⟨ψ 0 c 1 ψ i ⟩⟨ψ i c †*N*ψ 0 ⟩ + ⟨ψ 0 c †*N*ψ i ⟩⟨ψ i c 1 ψ 0 ⟩ ki + ⟨l, r ... = 1 √ 2 (b ± L+1−*n*,L+1+*n*+ b ± L−*n*,L+2+*n*), (E5) with b ± i,j defined in Eq. (6). (2.-) Case γ = 1. ...##
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Building an adiabatic quantum computer simulation in the classroom

2018
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American Journal of Physics
*

*N*.

*Santalla*... Let

*N*be our target number. If

*N*¼ pq, with p q integers, then p

*N*1=2 . For example, if

*N*¼ 33, then any factor should be smaller than 33 1=2 < 6. ...

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Random walkers on a deformable medium
[article]

2020
*
arXiv
*
pre-print

In this case, the curves for different

arXiv:2004.02236v2
fatcat:vcadsfpxxjhd3nvje32bc7hhaq
*N*P do not collapse unless we scale differently the time axis (dividing by*N*P ) and σ S [*N*J ], which should be divided by*N*1/2 P , as we show in the inset. ... Fig. 6 (top) represents the expected value, E S [*N*J ], scaled with the number of particles*N*P , as a function of time, also divided by*N*P . ...##
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First-Passage Percolation under extreme disorder: from bond-percolation to Kardar-Parisi-Zhang universality
[article]

2019
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arXiv
*
pre-print

As as consequence, for extreme disorder the mean arrival time is not well-defined and its average value is dominated by the largest value: T (x) = 1

arXiv:1912.08192v1
fatcat:czhrhdxrivbz3mh2ssglqbmvnm
*N**N*i T i (x) 1*N*T max*N*(x), where T max*N*(x) = max ... universal curve if we rescale the size s by s o , and*n*s by*n*so . ...
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