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Entanglement links and the quasiparticle picture [article]

Silvia N. Santalla, Giovanni Ramírez, Sudipto Singha Roy, Germán Sierra, Javier Rodríguez-Laguna
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.  ... 
arXiv:2208.03766v1 fatcat:d5wscmo635g2rnrfonx3ijn2vi

Symmetry protected phases in inhomogeneous spin chains [article]

Nadir Samos Sáenz de Buruaga, Silvia N. Santalla, Javier Rodríguez-Laguna, Germán Sierra
2018 arXiv   pre-print
L−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).  ... 
arXiv:1812.04869v1 fatcat:knvzr32kxnesbcwaslmihl6mbm

Entanglement in non-critical inhomogeneous quantum chains [article]

Nadir Samos Sáenz de Buruaga, Silvia N. Santalla, Javier Rodríguez-Laguna, Germán Sierra
2021 arXiv   pre-print
Using Eq. (4) we have ∂ t α 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  ... 
arXiv:2107.12113v1 fatcat:h6fxjcdfcfakfczqqpdbb45d2u

Casimir forces on deformed fermionic chains

Begoña Mula, Silvia N. Santalla, Javier Rodríguez-Laguna
2021 Physical Review Research  
Rodríguez-López, 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 12N 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 12N 2 . ( 29 ) Thus we are led to the following claim:  ... 
doi:10.1103/physrevresearch.3.013062 fatcat:clnzzk57tvct3ftfgcufqfkosi

Power Accretion in Social Systems [article]

Silvia N. Santalla, Kostadin Koroutchev, Elka Korutcheva, Javier Rodriguez-Laguna
2019 arXiv   pre-print
Assuming that the effective number of agents is 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 [  ... 
arXiv:1902.03288v1 fatcat:yrsg272fhfbgtdev5wzsm7iztq

Entanglement as geometry and flow [article]

Sudipto Singha Roy, Silvia N. Santalla, Javier Rodríguez-Laguna, Germán Sierra
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^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  ... 
arXiv:1906.05146v1 fatcat:t5y2tcjrerc2tnq3v4eokbxhue

Depletion in fermionic chains with inhomogeneous hoppings [article]

Begoña Mula, Nadir Samos Sáenz de Buruaga, Germán Sierra, Silvia N. Santalla, Javier Rodríguez-Laguna
2022 arXiv   pre-print
Then, J n−1 ψ n−1 + J n ψ n+1 = Eψ n , (42) which can be rewritten for very smooth J as J nn−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  ... 
arXiv:2209.10624v1 fatcat:v3za64ssvnb3plpryyu4tmhs4q

Entanglement as geometry and flow

Sudipto Singha Roy, Silvia N. Santalla, Javier Rodríguez-Laguna, Germán Sierra
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 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.  ... 
doi:10.1103/physrevb.101.195134 fatcat:gcpi7bbdjvfdvlyi46jxd6f2va

Nanowire reconstruction under external magnetic fields [article]

Eva M. Fernández, Silvia N. Santalla, José Enrique Alvarellos, Javier Rodríguez-Laguna
2020 arXiv   pre-print
We can write now: Z = {xi} V x1 T x1,x2 V x2 T x2,x3 V x3 · · · T x 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  ... 
arXiv:1910.04129v2 fatcat:i5h34pf4wrgijhahb7edzntyqm

Ergotropy and entanglement in critical spin chains [article]

Begoña Mula, Eva M. Fernández, José E. Alvarellos, Julio J. Fernández, David García-Aldea, Silvia N. Santalla, Javier Rodríguez-Laguna
2022 arXiv   pre-print
Sierra and 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  ... 
arXiv:2207.13998v1 fatcat:s66sh43ypvdpha6jwdhsvuco6e

Casimir forces on deformed fermionic chains [article]

Begoña Mula, Silvia N. Santalla, Javier Rodríguez-Laguna
2020 arXiv   pre-print
Rodríguez-López, N. Samos Sáenz de Buruaga and G. Sierra for very useful discussions.  ...  J N J N − π 12N 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 NN J N , so we obtain F N ≈ −c 0 − B 2 J N J N + π 12N 2 . (12) The validity of expression (12) can be checked  ... 
arXiv:2004.12456v2 fatcat:clsgzlza5nggxpurc5h33nq2im

Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect [article]

Nadir Samos Sáenz de Buruaga, Silvia N. Santalla, Javier Rodríguez-Laguna, Germán Sierra
2019 arXiv   pre-print
c † 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.  ... 
arXiv:1912.10788v1 fatcat:jingtiji5zginmgkzpf7q3npmy

Building an adiabatic quantum computer simulation in the classroom

Javier Rodríguez-Laguna, Silvia N. Santalla
2018 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.  ... 
doi:10.1119/1.5021360 fatcat:rtkndwpntnhhffpej3wt7ax3te

Random walkers on a deformable medium [article]

Carlos Lajusticia-Costan, Silvia N. Santalla, Javier Rodríguez-Laguna, Elka Korutcheva
2020 arXiv   pre-print
In this case, the curves for different 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 .  ... 
arXiv:2004.02236v2 fatcat:vcadsfpxxjhd3nvje32bc7hhaq

First-Passage Percolation under extreme disorder: from bond-percolation to Kardar-Parisi-Zhang universality [article]

Daniel Villarrubia, Iván Álvarez Domenech, Silvia N. Santalla, Javier Rodríguez-Laguna, Pedro Córdoba-Torres
2019 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 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 .  ... 
arXiv:1912.08192v1 fatcat:czhrhdxrivbz3mh2ssglqbmvnm
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