Ground state entanglement energetics

Büttiker, Μ.; Jordan, Andrew N.

doi:10.1016/j.physe.2005.05.024

Cited by 23 publications

(22 citation statements)

References 44 publications

(51 reference statements)

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“…Considering the subsystems Hamiltonian H s as an observable of interest, projective measurements of H s can find the system in higher energy states even at zero temperature [24,25]. This is the case when subsystem and environment are entangled and therefore the ground state does not factorize into a product of a system wave function and a bath wave function.…”

Section: B Ground State Energetics At Zero Temperaturementioning

confidence: 99%

Information and Entropy in Quantum Brownian Motion

Hörhammer¹,

Büttner²

2008

J Stat Phys

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We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two entropies which are due to the fact that the Brownian particle and its environment are entangled. We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic properties, as it is the case for the Landauer principle.

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Section: B Ground State Energetics At Zero Temperaturementioning

confidence: 99%

Information and Entropy in Quantum Brownian Motion

Hörhammer¹,

Büttner²

2008

J Stat Phys

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“…A slightly different formulation of the concept of entanglement Hamiltonians was also considered earlier in Refs. [33,34].…”

mentioning

confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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“…In fact, since |E 0 a ⊗ |0 f is not the eigenstate of the full Hamiltonian of the atom-field system -this is particularly conspicuous at strong coupling -it can not be the lowest energy state of the combined system per se. As a matter of fact, the true ground state of the combined system is an entangled state of the free atomic state and the field state [70][71][72]. Thus the product state |E 0 a ⊗|0 f appears as an excited state for the combined system.…”

Section: B Entangled Statementioning

confidence: 99%