Matrix product states and exactly solvable spin 1/2 Heisenberg chains with nearest neighbor interactions

Abstract

Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in compact form. The ground state has a very interesting property: all the pairs of spins are equally entangled with each other. Therefore it is possible to engineer long-range entanglement in experimentally realizable spin systems on the one hand and study more closely quantum phase transition in such systems on the other.

4 pages, RevTex, references added, improved presentation, typos fixed

References in corpus (2)

• Entanglement versus Correlations in Spin Systems
• Diverging Entanglement Length in Gapped Quantum Spin Systems

Cited by in corpus (12)

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• Bell-CHSH function approach to quantum phase transitions in matrix product systems
• Exact symmetry breaking ground states for quantum spin chains
• Frustration-free Hamiltonians supporting Majorana zero edge modes
• Exact ground states for two new spin-1 quantum chains, new features of matrix product states
• A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices
• Classification of matrix product ground states corresponding to one dimensional chains of two state sites of nearest neighbor interactions
• Interrelations among frustration-free models via Witten's conjugation
• A new family of matrix product states with Dzyaloshinski-Moriya interactions