Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

ENTANGLEMENT PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS

J. W. CLARK, Aikaterini Mandilara, MANFRED L. RISTIG, K. E. Kürten

Published Aug 20, 2009• 0 citations
Publisher

Abstract

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

DOI
10.1142/s0217979209063249

Related papers

Entanglement Properties Of Quantum Many-Body Wave Functions

J. W. Clark, Aikaterini Mandilara, MANFRED L. RISTIG

Entanglement properties of the trial many-body wave functions in variational treatments of the transverse Ising model in two, three, and four dimensions are investigated. Based on data for magnetizations and correlation functions generated by for symmetry-breaking Hartree-Jastrow trial ground states, results are presented for several measures of bipartite entanglement, including the von Neumann entropy of a single spin in the lattice, the concurrence between two spins, and a lower bound on the localizable entanglement, as functions of coupling strength. A simple relation is established between the Hartree-Jastrow states and the nilpotent polynomial representation of multipartite entanglement. In addition, some general comments are made on the entanglement properties of classes of many-body wave functions commonly adopted in theories of strongly correlated quantum systems.

arXiv:cond-mat/0512558•Dec 21, 2005•1 citation

Strongly Correlated Systems, Transport, Entanglement, and Dynamics

Younes Javanmard

Strongly correlated systems, i.e., quantum materials for which the interactions between its constituents are strong, are good candidates for the development of applications based on quantum-mechanical principles, such as quantum computers. Two paradigmatic models of strongly correlated systems are heavy-fermionic systems and one-dimensional spin-12 systems, with and without quenched disorder. In the past decade, improvement in computational methods and a vast enhancement in computational power has made it possible to study these systems in a a non-perturbative manner. In this thesis we present state-of-the-art numerical methods to investigate the properties of strongly correlated systems, and we apply these methods to solve a couple of selected problems in quantum condensed matter theory. We start by revisiting the phase diagram of the Falicov-Kimball model on the square lattice which can be considered as a heavy-fermionic systems. This model describes an interplay between conduction electrons and heavy electrons and reveals several distinct metal-insulator phase transitions. Using a lattice Monte-Carlo method, we study the transport properties of the model. Our analysis describes the role of temperature and interaction strength on the metal-insulator phase transitions in the Falicov-Kimball model. The second part of the thesis investigate the spatial structure of the entanglement in ground and thermal statesof the transverse-field Ising chain. We use the logarithmic negativity as a measure for the entanglement between two disjoint blocks. We investigate how logarithmic negativity depends on the spatial separation between two blocks, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled. Our results hold even in the presence of long-ranged quantum correlations, i.e., at the system’s quantum critical point. Using Time-Evolving Block Decimation (TEBD), we explore this feature as a function of temperature and size of the two blocks. We present a simple model to describe our numerical observations. In the last part of this thesis, we introduce an order parameter for a many-body localized spin-glass (MBL-SG) phase. We show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains, both in many-body eigenstates as well as in the nonequilibrium dynamics, from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.

•Aug 30, 2018•0 citations

Many-body physics from a quantum information perspective

Maciej Lewenstein, Anna Sanpera, V. Ahufinger

This chapter deals with the novel characterisation of many-body physics using tools from quantum information theory. The first part focuses on the theory of entanglement, where the basic notions as bipartite versus multipartite entanglement, measures of entanglement, and the link between entangled states completely positive maps are discussed. The second part deals with the concept of area law, relating the von Neumann measure of the entropy of a subsystem with the size of the system for gapped, critical, and topological systems. The entanglement content in critical quantum systems is studied in reference to quantum phase transitions. Finally, the round states of many-body systems with a tensor network representation are described.

Oxford University Press eBooks•Mar 8, 2012•0 citations

Entanglement in strongly fluctuating quantum many-body states

Weifei Li

In this thesis, the scaling behavior of entanglement is investigated in quantum systems with strongly fluctuating ground states. We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way, and calculate exactly the scaling of the entanglement entropy of finite systems in an infinite universe. In these systems, we observe quantum phase transition by tuning the parameters of the Hamiltonian. Our study shows that although in one dimension there is a unique relation between the quantum phase transition and the scaling behavior of entanglement, this is not necessarily true in higher dimensions.

•Jan 1, 2015•0 citations

Entanglement and Correlations in Cold Atomic Systems

M. Popp

This thesis is devoted to the theoretical characterization and generation of strongly correlated many-body states from the perspective of quantum information theory.We first study the entanglement properties of general many-body states and define a new measure for multipartite entanglement, the "Localizable Entanglement (LE)".It quantifies the maximal entanglement that can be localized, on average, between two parties by performing local measurements on the other parties.This measure provides knowledge of the "entanglement length", which is of particular importance in the context of quantum repeaters for long-distance quantum communication.We prove upper and lower bounds on LE in terms of two-body correlation functions and develop a method for the numerical computation of LE in one-dimensional spin systems.We analyze the localizable entanglement in various spin systems and observe characteristic features for a quantum phase transition such as a diverging entanglement length.In the second part of the thesis we focus on a specific many-body system: ultra-cold atoms in an optical lattice.This system is a promising candidate for the first physical realization of a "quantum simulator", but the temperature in current experiments is still too high.We propose, analyze and compare several schemes to cool the atoms close to the ground state of the strong interaction regime.In particular, we devise an algorithmic cooling protocol that combines occupation number filtering with spin-dependent lattice shifts.In addition, we propose two different physical realizations of filtering and also design protocols that generate an ensemble of quantum registers for quantum computation.In the third part we propose how to create entanglement in small atomic clouds by deforming and rotating the harmonic trapping potential.The resulting states are entangled in their motional degrees of freedom and can be identified with strongly correlated fractional quantum Hall states.For the case of two, three and four atoms we show how to adiabatically transform the unentangled ground state into the desired entangled state.We further discuss characteristic features of these states and propose how to create and detect them experimentally using an optical lattice setup. A Proof of the lower bound on LEA.1 Theorem on connected correlation functions and local measurements . . . . . . . . .

•Jan 1, 2006•0 citations

GENERALIZED ENTANGLEMENT AND QUANTUM PHASE TRANSITIONS

Rolando D. Somma, Howard Barnum, Emanuel H. Knill +2 more

Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.

International Journal of Modern Physics B•Jul 30, 2006•2 citations
The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.
Entanglement properties of the trial many-body wave functions in variational treatments of the transverse Ising model in two, three, and four dimensions are investigated. Based on data for magnetizations and correlation functions generated by for symmetry-breaking Hartree-Jastrow trial ground states, results are presented for several measures of bipartite entanglement, including the von Neumann entropy of a single spin in the lattice, the concurrence between two spins, and a lower bound on the localizable entanglement, as functions of coupling strength. A simple relation is established between the Hartree-Jastrow states and the nilpotent polynomial representation of multipartite entanglement. In addition, some general comments are made on the entanglement properties of classes of many-body wave functions commonly adopted in theories of strongly correlated quantum systems.
Strongly correlated systems, i.e., quantum materials for which the interactions between its constituents are strong, are good candidates for the development of applications based on quantum-mechanical principles, such as quantum computers. Two paradigmatic models of strongly correlated systems are heavy-fermionic systems and one-dimensional spin-12 systems, with and without quenched disorder. In the past decade, improvement in computational methods and a vast enhancement in computational power has made it possible to study these systems in a a non-perturbative manner. In this thesis we present state-of-the-art numerical methods to investigate the properties of strongly correlated systems, and we apply these methods to solve a couple of selected problems in quantum condensed matter theory. We start by revisiting the phase diagram of the Falicov-Kimball model on the square lattice which can be considered as a heavy-fermionic systems. This model describes an interplay between conduction electrons and heavy electrons and reveals several distinct metal-insulator phase transitions. Using a lattice Monte-Carlo method, we study the transport properties of the model. Our analysis describes the role of temperature and interaction strength on the metal-insulator phase transitions in the Falicov-Kimball model. The second part of the thesis investigate the spatial structure of the entanglement in ground and thermal statesof the transverse-field Ising chain. We use the logarithmic negativity as a measure for the entanglement between two disjoint blocks. We investigate how logarithmic negativity depends on the spatial separation between two blocks, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled. Our results hold even in the presence of long-ranged quantum correlations, i.e., at the system’s quantum critical point. Using Time-Evolving Block Decimation (TEBD), we explore this feature as a function of temperature and size of the two blocks. We present a simple model to describe our numerical observations. In the last part of this thesis, we introduce an order parameter for a many-body localized spin-glass (MBL-SG) phase. We show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains, both in many-body eigenstates as well as in the nonequilibrium dynamics, from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.
This chapter deals with the novel characterisation of many-body physics using tools from quantum information theory. The first part focuses on the theory of entanglement, where the basic notions as bipartite versus multipartite entanglement, measures of entanglement, and the link between entangled states completely positive maps are discussed. The second part deals with the concept of area law, relating the von Neumann measure of the entropy of a subsystem with the size of the system for gapped, critical, and topological systems. The entanglement content in critical quantum systems is studied in reference to quantum phase transitions. Finally, the round states of many-body systems with a tensor network representation are described.
In this thesis, the scaling behavior of entanglement is investigated in quantum systems with strongly fluctuating ground states. We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way, and calculate exactly the scaling of the entanglement entropy of finite systems in an infinite universe. In these systems, we observe quantum phase transition by tuning the parameters of the Hamiltonian. Our study shows that although in one dimension there is a unique relation between the quantum phase transition and the scaling behavior of entanglement, this is not necessarily true in higher dimensions.
This thesis is devoted to the theoretical characterization and generation of strongly correlated many-body states from the perspective of quantum information theory.We first study the entanglement properties of general many-body states and define a new measure for multipartite entanglement, the "Localizable Entanglement (LE)".It quantifies the maximal entanglement that can be localized, on average, between two parties by performing local measurements on the other parties.This measure provides knowledge of the "entanglement length", which is of particular importance in the context of quantum repeaters for long-distance quantum communication.We prove upper and lower bounds on LE in terms of two-body correlation functions and develop a method for the numerical computation of LE in one-dimensional spin systems.We analyze the localizable entanglement in various spin systems and observe characteristic features for a quantum phase transition such as a diverging entanglement length.In the second part of the thesis we focus on a specific many-body system: ultra-cold atoms in an optical lattice.This system is a promising candidate for the first physical realization of a "quantum simulator", but the temperature in current experiments is still too high.We propose, analyze and compare several schemes to cool the atoms close to the ground state of the strong interaction regime.In particular, we devise an algorithmic cooling protocol that combines occupation number filtering with spin-dependent lattice shifts.In addition, we propose two different physical realizations of filtering and also design protocols that generate an ensemble of quantum registers for quantum computation.In the third part we propose how to create entanglement in small atomic clouds by deforming and rotating the harmonic trapping potential.The resulting states are entangled in their motional degrees of freedom and can be identified with strongly correlated fractional quantum Hall states.For the case of two, three and four atoms we show how to adiabatically transform the unentangled ground state into the desired entangled state.We further discuss characteristic features of these states and propose how to create and detect them experimentally using an optical lattice setup. A Proof of the lower bound on LEA.1 Theorem on connected correlation functions and local measurements . . . . . . . . .
Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.