Quantum Phase Transitions and Matrix Product States in Spin Ladders

Abstract

We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such models. We also study the behavior of entanglement of different neighboring sites near the transition point and show that quantum phase transitions in these systems are accompanied by divergences in derivatives of entanglement.

20 pages, 6 figures, essential changes (i.e derivation of the Hamiltonian), Revtex

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Cited by in corpus (14)

• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• The matrix product representations for all valence bond states
• Entanglement and quantum phase transitions in matrix product spin one chains
• Efficient evaluation of high-order moments and cumulants in tensor network states
• Entanglement and fidelity signatures of quantum phase transitions in spin liquid models
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Bell-CHSH function approach to quantum phase transitions in matrix product systems
• Exact dimer ground states for a continuous family of quantum spin chains
• Exact symmetry breaking ground states for quantum spin chains
• 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
• Low energy properties of non-perturbative quantum systems: a space reduction approach
• Spatial reflection and renormalization group flow of quantum many-body systems with matrix product state representation
• A new family of matrix product states with Dzyaloshinski-Moriya interactions