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DANIEL SÁNCHEZ PEACHAM
DANIEL SÁNCHEZ PEACHAM

2020-01-31
CHRISTOS CHARALAMBOUS
CHRISTOS CHARALAMBOUS

2020-02-06
SERGIO LUCIO DE BONIS
SERGIO LUCIO DE BONIS

2020-02-10
JULIO SANZ SÁNCHEZ
JULIO SANZ SÁNCHEZ

2020-02-17
SANDRA DE VEGA
SANDRA DE VEGA

2020-02-21
ESTHER GELLINGS
ESTHER GELLINGS

2020-03-26
NICOLA DI PALO
NICOLA DI PALO

2020-03-30
ANGELO PIGA
ANGELO PIGA

2020-04-24
PABLO GOMEZ GARCIA
PABLO GOMEZ GARCIA

2020-06-04
ANUJA ARUN PADHEY
ANUJA ARUN PADHEY

2020-06-08
VIKAS REMESH
VIKAS REMESH

2020-06-23
DAVID ALCARAZ
DAVID ALCARAZ

2020-06-30
GERARD PLANES
GERARD PLANES

2020-07-09
IRENE ALDA
IRENE ALDA

2020-07-13
EMANUELE TIRRITO
EMANUELE TIRRITO

2020-07-16
ALBERT ALOY
ALBERT ALOY

2020-07-27
MARIA SANZ-PAZ
MARIA SANZ-PAZ

2020-07-28
JUAN MIGUEL PÉREZ ROSAS
JUAN MIGUEL PÉREZ ROSAS

2020-10-08
ZAHRA RAISSI
ZAHRA RAISSI

2020-10-30
IVAN BORDACCHINI
IVAN BORDACCHINI

2020-11-09
GORKA MUÑOZ GIL
GORKA MUÑOZ GIL

2020-11-17
ZAHRA KHANIAN
ZAHRA KHANIAN

2020-11-27
PAMINA WINKLER
PAMINA WINKLER
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2020-12-02
BIPLOB NANDY
BIPLOB NANDY
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2020-12-11
DANIEL GONZÁLEZ CUADRA
DANIEL GONZÁLEZ CUADRA
Entanglement and Bell Correlations in Strongly Correlated Many-Body Quantum Systems


Dr Angelo Piga
March 30th, 2020
ANGELO PIGA
Quantum Optics Theory
ICFO-The Institute of Photonic Sciences
During the past two decades, thanks to the mutual fertilization of the research in quantum information and condensed matter, new approaches based on purely quantum features without any classical analog turned out to be very useful in the characterization of many-body quantum systems (MBQS). A peculiar role is obviously played by the study of purely quantum correlations, manifesting in the “spooky” properties of entanglement and nonlocality (or Bell correlations), which ultimately discriminate classical from quantum regimes. It is, in fact, such kind of correlations that give rise to the plethora of intriguing emergent behaviors of MBQS, which cannot be reduced to a mere sum of the behaviors of individual components, the most important example being the quantum phase transitions. However, despite being indeed closely related concepts, entanglement and nonlocality are actually two different resources.
With regard to the entanglement, we will use it to characterize several instances of MBQS, to exactly locate and characterize quantum phase transitions in spin-lattices and interacting fermionic systems, to classify different gapped quantum phases according to their topological features and to provide a purely quantum signature of chaos in dynamical systems.
Our approach will be mainly numerical and for simulating the ground states of several one-dimensional lattice systems we draw heavily on the celebrated “density matrix renormalization group” (DMRG) algorithm in the “matrix product state” (MPS) ansatz. A MPS is a one-dimensional tensor network (TN) representation for quantum states and occupies a pivotal position in what we have gained in thinking MBQS from an entanglement perspective. In fact, the success of TNs states mainly relies on their fulfillment, by construction, of the socalled “entanglement area law”. This is a feature shared by the ground states of gapped Hamiltonians with short-range interactions among the components and consists of a sub-extensive entanglement entropy, which grows only with the surface of the bipartition. This property translates in a reduced complexity of such systems, allowing affordable simulations, with an exponential reduction of computational costs. Besides the use of already existing TN-based algorithms, an effort will be done to develop a new one suitable for high-dimensional lattices. While many useful results are available for the entanglement in many different contexts, less is known about the role of nonlocality. Formally, a state of a multi-party system is defined nonlocal if its correlations violate some “Bell inequality” (BI). The derivation of the BIs for systems consisting of many parties is a formidable task and only recently a class of them, relevant for nontrivial states, has been proposed. In an important chapter of the thesis, we apply these BIs to fully characterize the phase transition of a long-range ferromagnetic Ising model, doing a comparison with entanglement-based results and then making one of the first efforts in the study of MBQS from a nonlocality perspective.
Monday, March 30, 2020, 11:00. Online
Thesis Advisor: Prof Dr Maciej Lewenstien
Thesis Co-advisor: Dr Shi-ju Ran
ICFO-The Institute of Photonic Sciences
During the past two decades, thanks to the mutual fertilization of the research in quantum information and condensed matter, new approaches based on purely quantum features without any classical analog turned out to be very useful in the characterization of many-body quantum systems (MBQS). A peculiar role is obviously played by the study of purely quantum correlations, manifesting in the “spooky” properties of entanglement and nonlocality (or Bell correlations), which ultimately discriminate classical from quantum regimes. It is, in fact, such kind of correlations that give rise to the plethora of intriguing emergent behaviors of MBQS, which cannot be reduced to a mere sum of the behaviors of individual components, the most important example being the quantum phase transitions. However, despite being indeed closely related concepts, entanglement and nonlocality are actually two different resources.
With regard to the entanglement, we will use it to characterize several instances of MBQS, to exactly locate and characterize quantum phase transitions in spin-lattices and interacting fermionic systems, to classify different gapped quantum phases according to their topological features and to provide a purely quantum signature of chaos in dynamical systems.
Our approach will be mainly numerical and for simulating the ground states of several one-dimensional lattice systems we draw heavily on the celebrated “density matrix renormalization group” (DMRG) algorithm in the “matrix product state” (MPS) ansatz. A MPS is a one-dimensional tensor network (TN) representation for quantum states and occupies a pivotal position in what we have gained in thinking MBQS from an entanglement perspective. In fact, the success of TNs states mainly relies on their fulfillment, by construction, of the socalled “entanglement area law”. This is a feature shared by the ground states of gapped Hamiltonians with short-range interactions among the components and consists of a sub-extensive entanglement entropy, which grows only with the surface of the bipartition. This property translates in a reduced complexity of such systems, allowing affordable simulations, with an exponential reduction of computational costs. Besides the use of already existing TN-based algorithms, an effort will be done to develop a new one suitable for high-dimensional lattices. While many useful results are available for the entanglement in many different contexts, less is known about the role of nonlocality. Formally, a state of a multi-party system is defined nonlocal if its correlations violate some “Bell inequality” (BI). The derivation of the BIs for systems consisting of many parties is a formidable task and only recently a class of them, relevant for nontrivial states, has been proposed. In an important chapter of the thesis, we apply these BIs to fully characterize the phase transition of a long-range ferromagnetic Ising model, doing a comparison with entanglement-based results and then making one of the first efforts in the study of MBQS from a nonlocality perspective.
Monday, March 30, 2020, 11:00. Online
Thesis Advisor: Prof Dr Maciej Lewenstien
Thesis Co-advisor: Dr Shi-ju Ran