Entanglement over the rainbow

Ramírez, Giovanni; Rodríguez-Laguna, Javier; Sierra, Germȧn

doi:10.1088/1742-5468/2015/06/p06002

Cited by 62 publications

(102 citation statements)

References 27 publications

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“…Similarly it should work for the Jordan-Wigner transformed equivalent fermionic models with a disordered hopping parameter [46]. It should also be permissible to implement different forms of disorder, such as aperiodic sequences [47] as long as the singlet approximation is valid throughout the renormalization procedure.…”

Section: Discussionmentioning

confidence: 99%

Self-assembling tensor networks and holography in disordered spin chains

Goldsborough

Römer

2014

Phys. Rev. B

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We show that the numerical strong disorder renormalization group algorithm of Hikihara et al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions, and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder-averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems.

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Section: Discussionmentioning

confidence: 99%

Self-assembling tensor networks and holography in disordered spin chains

Goldsborough

Römer

2014

Phys. Rev. B

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“…20, chap. 6, Ramirez et al constructed mirror symmetric models satisfying the volume law, i.e., maximum scaling with the system's size possible (27). The models described above are all interesting for the intended purposes but either have very large spins (e.g., s ≥ 10) or involve some degree of fine-tuning.…”

Section: Significancementioning

confidence: 99%

Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

Movassagh

Shor

2016

Proc. Natl. Acad. Sci. U.S.A.

102

178

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Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an "area law": The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system's size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system's size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.quantum matter | local Hamiltonians entanglement entropy | area law | spin chains | Hamiltonian gap S tudy of quantum many-body systems (QMBSs) is the study of quantum properties of matter and quantum resources (e.g., entanglement) provided by matter for building revolutionary new technologies such as a quantum computer. One of the properties of the QMBS is the amount of entanglement among parts of the system (1, 2). Entanglement can be used as a resource for quantum technologies and information processing (2-5); however, at a fundamental level it provides information about the quantum state of matter, such as near-criticality (6, 7). Moreover, systems with high entanglement are usually hard to simulate on a classical computer (8). How much entanglement do natural QMBSs possess? What are the fundamental limits on simulation of physical systems?The area law says that entanglement entropy between two subsystems of a system is proportional to the area of the boundary between them. A generic state does not obey an area law (9); therefore, obeying an area law implies that a QMBS contains much less quantum correlation than generically expected. One can imagine that any given system has inherent constraints such as underlying symmetries and locality of interaction that restrict the states to reside on special submanifolds rendering their simulation efficient (10).Since the discovery that the Affleck-Kennedy-Lieb-Tasaki (AKLT) model (11) is exactly solvable, and that the density matrix re...

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“…Notice that entanglement properties of excited states of many-body Hamiltonians have attracted increasing attention recently [87,[104][105][106][107][108][109][110][111][112][113][114][115][116][117]. Figure 4 (a) plots the two-spin entropy S 2 versus E/L for different eigenstates of the XXX chain.…”

Section: Entanglement Propertiesmentioning

confidence: 99%

Eigenstate thermalization hypothesis and integrability in quantum spin chains

2015

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We investigate the eigenstate thermalization hypothesis (ETH) in integrable models, focusing on the spin-1 2 isotropic Heisenberg (XXX) chain. We provide numerical evidence that ETH holds for typical eigenstates (weak ETH scenario). Specifically, using a numerical implementation of state-of-the-art Bethe ansatz results, we study the finite-size scaling of the eigenstate-to-eigenstate fluctuations of the reduced density matrix. We find that fluctuations are normally distributed, and their standard deviation decays in the thermodynamic limit as L −1/2 , with L the size of the chain. This is in contrast with the exponential decay that is found in generic nonintegrable systems. Based on our results, it is natural to expect that this scenario holds in other integrable spin models and for typical local observables. Finally, we investigate the entanglement properties of the excited states of the XXX chain. We numerically verify that typical mid-spectrum eigenstates exhibit extensive entanglement entropy (i.e., volume-law scaling).

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Entanglement over the rainbow

Cited by 62 publications

References 27 publications

Self-assembling tensor networks and holography in disordered spin chains

Self-assembling tensor networks and holography in disordered spin chains

Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

Eigenstate thermalization hypothesis and integrability in quantum spin chains

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