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Register a new userRegional versus Global Entanglement in Resonating-Valence-Bond states
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Added by
Dagomir Kaszlikowski
Publication date
2007
fields
Physics
and research's language is
English
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We investigate the entanglement properties of resonating-valence-bond states on two and higher dimensional lattices, which play a significant role in our understanding of various many-body systems. We show that these states are genuinely multipartite entangled, while there is only a negligible amount of two-site entanglement. We comment on possible physical implications of our findings.
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Dickes original thought experiment with two spins coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to N spins and show that it naturally gives rise to highly entangled states. In particular, it gives rise to dark states which have resonating valence bond (RVB) character. We first consider a system of N two level spins in a cavity with only one spin in the excited state. This initial state is a linear combination of a dark state and a bright state. We point out the dark state is a coherent superposition of singlets with resonating valence bond character. We show that the coupling to the photon mode takes the spin system into a mixed state with an entangled density matrix. We next consider an initial state with half of the spins in the excited state. We show that there is a non-zero probability for this to collapse into a dark state with RVB character. In the lossy cavity limit, if no photon is detected within several decay time periods, we may deduce that the spin system has collapsed onto the dark RVB state. We show that the probability for this scales as 2/N, making it possible to generate RVB states of 20 spins or more.
The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.
Resonating valence bond (RVB) theory of high Tc superconductivity, an electron correlation based mechanism, began as an insightful response by Anderson, to Bednorz and Mullers discovery of high Tc superconductivity in cuprates in late 1986. Shortly a theoretical framework for quantum spin liquids and superconductivity was developed. This theory adresses a formidable strong coupling quantum manybody problem, in modern times. It is built on certain key experimental facts: i) survival of a dynamical Mott localization in a metallic state, ii) proliferation of bond singlets and iii) absence of fermi liquid quasi particles. After summarising RVB theory I will provide an aerial view of, mostly, new superconductors where I believe that, to a large degree RVB mechanism is at work and indicate prospects for even higher Tcs.
We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a single-determinant that is multiplied by a Jastrow correlation factor. Whereas the determinantal part incorporates static correlation effects, the augmented real-space correlation factor accounts for the dynamics electron correlation. The accuracy of this approach is demonstrated by computing the potential energy surface for the ozone molecule in three vibrational states: symmetric, asymmetric and scissoring. We find that the employed wave function provides a detailed description of rather strongly-correlated multi-reference systems, which is in quantitative agreement with experiment.
Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with two-fold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical $Z$-rotation by angle $frac{2pi}{N}$, for any integer $N > 2$, is provided by a global twist operation, which is of topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.
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