scholarly journals Structural and magnetic instabilities of two-dimensional quantum spin systems

2006 ◽  
Vol 74 (1) ◽  
Author(s):  
Carsten H. Aits ◽  
Ute Löw ◽  
Andreas Klümper ◽  
Werner Weber
Keyword(s):  
Quantum Spin ◽  
Spin Systems ◽  
Two Dimensional ◽  
Quantum Spin Systems

The complexity of quantum spin systems on a two-dimensional square lattice

2008 ◽  
Vol 8 (10) ◽  
pp. 900-924
Author(s):  
R. Oliveira ◽  
B.M. Terhal
Keyword(s):  
Perturbation Method ◽  
Quantum Computation ◽  
Quantum Spin ◽  
Circuit Model ◽  
Spin Systems ◽  
Square Lattice ◽  
Two Dimensional ◽  
Quantum Spin Systems ◽  
Local Interactions ◽  
Side Result

The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.

scholarly journals Two-Dimensional Quantum Spin Systems with Ladder and Plaquette Structures

1999 ◽  
Vol 68 (2) ◽  
pp. 642-649 ◽  
Author(s):  
Akihisa Koga ◽  
Seiya Kumada ◽  
Norio Kawakami
Keyword(s):  
Quantum Spin ◽  
Spin Systems ◽  
Two Dimensional ◽  
Quantum Spin Systems

scholarly journals An -valued index of symmetry-protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems

2021 ◽  
Vol 9 ◽  
Author(s):  
Yoshiko Ogata
Keyword(s):  
Finite Group ◽  
Quantum Spin ◽  
Spin Systems ◽  
Group Symmetry ◽  
Topological Phases ◽  
Two Dimensional ◽  
Quantum Spin Systems ◽  
Symmetry Protected

Abstract We consider symmetry-protected topological phases with on-site finite group G symmetry $\beta $ for two-dimensional quantum spin systems. We show that they have $H^{3}(G,{\mathbb T})$ -valued invariant.

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