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Volumn 73, Issue 9, 2006, Pages

Matrix product states represent ground states faithfully

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EID: 33645062947     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.73.094423     Document Type: Article
Times cited : (789)

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    • We choose the 1 L dependence such as to assure that the absolute error in extensive observables does not grow.
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    • Let us, e.g., specify a method which should in principle not get trapped in local minima. As in the adiabatic theorem, we can construct a time-dependent Hamiltonian H(t) with H(0) trivial and H(1) the Hamiltonian to simulate; if we discretize this evolution in a number of steps that grows polynomially in the inverse gap, the adiabatic theorem guarantees that we will end up in the ground state of H(1) if we can follow the ground state of H(t) closely. The idea is to make D of ψD (t) large enough such as to follow the ground state ψ(t) close enough in such a way that the optimization is always convex around the global optimum within the domain χ-ψ(t)≤.
    • Let us, e.g., specify a method which should in principle not get trapped in local minima. As in the adiabatic theorem, we can construct a time-dependent Hamiltonian H(t) with H(0) trivial and H(1) the Hamiltonian to simulate; if we discretize this evolution in a number of steps that grows polynomially in the inverse gap, the adiabatic theorem guarantees that we will end up in the ground state of H(1) if we can follow the ground state of H(t) closely. The idea is to make D of ψD (t) large enough such as to follow the ground state ψ(t) close enough in such a way that the optimization is always convex around the global optimum within the domain χ-ψ(t)≤.
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