Replacing energy by von Neumann entropy in quantum phase transitions

Kopp, Angela; Jia, Xun; Chakravarty, Sudip

doi:10.1016/j.aop.2006.08.002

Cited by 40 publications

(59 citation statements)

References 32 publications

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“…(32)). The previous expression allows At the transition point the entropy is discontinuous with a jump given by (Kopp et al, 2006) ∆S = ln 2 + δ/4δ c ln(δ/δ c ) (δ c is a high energy cutoff). A systematic analisys of the entropy in the spin-boson model for different coupling regimes was pursued recently in (K.Le Hur et al, 2007;Kopp and Le Hur, 2007).…”

Section: E Spin-boson Systemsmentioning

confidence: 99%

“…(32)) was studiedby numerical renormalization group in (Costi and McKenzie, 2003). An analytic calculation, including other dissipative models, has been presented in (Stauber and Guinea, 2004) and more recently in (Kopp et al, 2006;Stauber and Guinea, 2006a,b). In the broken-symmetry state has an effective classical description and the corresponding von Neumann entropy is zero.…”

Section: E Spin-boson Systemsmentioning

confidence: 99%

“…The entanglement entropy was studied for the Jaynes-Cummings , Tavis-Cummings model (Lambert et al, 2004(Lambert et al, , 2005 and for the spin-boson model (Costi and McKenzie, 2003;Jordan and Buttiker, 2004;Kopp et al, 2006;Stauber and Guinea, 2006a). Lambert and coworkers analyzed how the super-radiant quantum phase transition manifests in the entanglement between the atomic ensemble and the field mode.…”

Section: E Spin-boson Systemsmentioning

confidence: 99%

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Entanglement in many-body systems

Amico¹,

et al. 2008

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The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermion and boson model systems. Both bipartite and multipartite entanglement will be considered. In equilibrium we show how entanglement is tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.

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Section: E Spin-boson Systemsmentioning

confidence: 99%

Section: E Spin-boson Systemsmentioning

confidence: 99%

Section: E Spin-boson Systemsmentioning

confidence: 99%

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Entanglement in many-body systems

Amico¹,

et al. 2008

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“…It is important to remark that the validity of the metrics is independent from the specific form adopted; in order to verify this assumption, we measure the discrepancies of two potential energy distributions using the Rényi generalized divergence R d (Rényi, 1961) and the von Neumann divergence VN d (Kopp, Jia, & Chakravarty, 2007).…”

Section: The Relative Entropymentioning

confidence: 99%

Computational energy-based redesign of robust proteins

Stracquadanio¹,

Nicosia²

2011

Computers & Chemical Engineering

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“…6,7 When the two levels of the qubit are degenerate, the entanglement between the qubit and the bosons is discontinuous at this transition. 8,9 Here we report the first rigorous analytical results for the entanglement (quantum entropy) in the strongly entangled regime 1 − α ≫ ∆/ω c .…”

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confidence: 99%

Universal and Measurable Entanglement Entropy in the Spin-Boson Model

Kopp

Hur

2007

Phys. Rev. Lett.

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We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin E(α, ∆, h), where α is the dissipation strength, ∆ is the tunneling amplitude between qubit states, and h is the level asymmetry. For 1 − α ≫ ∆/ωc and (∆, h) ≪ ωc, we show that the Kondo energy scale TK controls the entanglement between the qubit and the bosonic environment (ωc is a high-energy cutoff). For h ≪ TK, the disentanglement proceeds as (h/TK ) 2 ; for h ≫ TK, E vanishes as (TK/h) 2−2α , up to a logarithmic correction. For a given h, the maximum entanglement occurs at a value of α which lies in the crossover regime h ∼ TK . We emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise. The concept of quantum entropy appears in multiple contexts, from black hole physics 1 to quantum information theory, where it measures the entanglement of quantum states.2 Prompted by the link between entanglement and quantum criticality, 3 a number of researchers have begun to study the entanglement entropy of condensed matter systems. In this Letter, we employ the spin-boson model 4,5 to describe the entanglement between a qubit (two-level system) and an infinite collection of bosons. With an Ohmic bosonic bath, the spin-boson model undergoes a quantum phase transition of Kosterlitz-Thouless type when α − 1 = ∆/ω c , where α is the strength of the coupling to the environment, ∆ is the tunneling amplitude between the qubit states, and ω c ≫ ∆ is an ultraviolet cutoff.6,7 When the two levels of the qubit are degenerate, the entanglement between the qubit and the bosons is discontinuous at this transition.8,9 Here we report the first rigorous analytical results for the entanglement (quantum entropy) in the strongly entangled regime 1 − α ≫ ∆/ω c .We exploit a mapping between the spin-boson model and the anisotropic Kondo model; our results follow from the Bethe ansatz solution of the equivalent interacting resonant level model. 10,11 We show that the entropy of entanglement (E) of the qubit with the environment is controlled by the Kondo energy scale T K

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Replacing energy by von Neumann entropy in quantum phase transitions

Cited by 40 publications

References 32 publications

Entanglement in many-body systems

Entanglement in many-body systems

Computational energy-based redesign of robust proteins

Universal and Measurable Entanglement Entropy in the Spin-Boson Model

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