2020
Roy, Sudipto Singha; Santalla, Silvia N.; Rodríguez-Laguna, Javier; Sierra, Germán
Entanglement as geometry and flow Journal Article
In: Physical Review B, vol. 101, no. 19, 2020.
@article{Singha_Roy_2020,
title = {Entanglement as geometry and flow},
author = {Sudipto Singha Roy and Silvia N. Santalla and Javier Rodríguez-Laguna and Germán Sierra},
url = {https://arxiv.org/abs/1906.05146},
doi = {10.1103/physrevb.101.195134},
year = {2020},
date = {2020-05-01},
urldate = {2020-05-01},
journal = {Physical Review B},
volume = {101},
number = {19},
publisher = {American Physical Society (APS)},
abstract = {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 of a (generalized) adjacency matrix. In the cases where the representation is exact, the elements of that matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all the cases it yields a natural entanglement contour which is similar to previous proposals.Moreover, for one-dimensional conformal invariant systems, the generalized adjacency matrix is given by the two-point correlator of an entanglement current operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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 of a (generalized) adjacency matrix. In the cases where the representation is exact, the elements of that matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all the cases it yields a natural entanglement contour which is similar to previous proposals.Moreover, for one-dimensional conformal invariant systems, the generalized adjacency matrix is given by the two-point correlator of an entanglement current operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.
2018
Xavier, J. C.; Alcaraz, F. C.; Sierra, G.
Equipartition of the entanglement entropy Journal Article
In: Physical Review B, vol. 98, no. 4, 2018.
@article{Xavier_2018,
title = {Equipartition of the entanglement entropy},
author = {J. C. Xavier and F. C. Alcaraz and G. Sierra},
url = {https://arxiv.org/abs/1804.06357},
doi = {10.1103/physrevb.98.041106},
year = {2018},
date = {2018-07-01},
urldate = {2018-07-01},
journal = {Physical Review B},
volume = {98},
number = {4},
publisher = {American Physical Society (APS)},
abstract = {The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one dimensional systems. We find surprisingly that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term, that depends on the central charge c, minus a double logarithmic correction related to the zero temperature susceptibility. This result provides a new method to estimate simultaneously the central charge c and the critical exponents of U(1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one dimensional systems. We find surprisingly that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term, that depends on the central charge c, minus a double logarithmic correction related to the zero temperature susceptibility. This result provides a new method to estimate simultaneously the central charge c and the critical exponents of U(1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.
Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán
Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems Journal Article
In: Journal of Statistical Mechanics: Theory and Experiment, vol. 2018, no. 4, pp. 043105, 2018.
@article{Tonni_2018,
title = {Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems},
author = {Erik Tonni and Javier Rodríguez-Laguna and Germán Sierra},
url = {https://arxiv.org/abs/1712.03557},
doi = {10.1088/1742-5468/aab67d},
year = {2018},
date = {2018-04-01},
urldate = {2018-04-01},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
volume = {2018},
number = {4},
pages = {043105},
publisher = {IOP Publishing},
abstract = {Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.